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Please tell me the correct working temperature range of tires. For example, kc3?

the most go kart tyres are working best at temp range of 43 - 54 Celsius (110 - 130 F).
Soft compounds favour higher temperatures and hard achieve lower temps. The rule "the softer tire the more grip" doesn't tell always the truth because in some cases the softer compound may go beyond the optimal temp range and the tires will start to lose their grip. A general rule is that you may go as soft as you can go near the above limit (approx 54 C) to get the best from your tires. Another big parameter is the pressure. The higher the pressure the more the temp rises, so if you are in qualifying you put a very soft compound with high pressures and in the race (15-20 laps) you run a harder compound (in order to last longer) with lower pressure. After the race you take the hot pressure of the tires (you must see a difference of 1-2 psi) and the temperature across the pattern. If the inner is about 1-3 degrees higher than the outer then it's ok. Some example to help you..

(Outer-Middle-Inner) : 41-42-43 = too low temps, try a softer compound or increase the pressure
                                    47-51-49 = good overall temp, lower the pressure
                                    46-43-48 = good overall temp, increase the pressure. If the overall temp exceed 54 then try a harder compound
                                    49-51-52 = just about the right compound and pressure

i'll try to make a review for tires in the next days to show the differences in the 12 different compounds in KRP. But i need time by then

great write up.. i thought 50mm medium was the next step down from 50mm hard but now i know is 40mm hard thanks!!

Thanks Evo 
To tell the truth the difference between 40 hard and 50 medium isn't quite noticeable (rigidity and weight are about the same). Personally i prefer starting with 40 hard in Lonato and when the track gains rubber i go to the pits and change to a 50 medium. I found in that way that my tires aren't struggling for grip when i start. You may also try begin with 50 hard but i dont prefer to mine because im having troubles in the first laps on most corner exits, the kart is pushing badly.

[cold]

Hey guys, im happy knowing that i could help you with my effort. This is a very long chapter and contains many physics and dynamics which are very confusing but with a lot of reading and a little effort we'll try to explore the "mysterious" world of go kart axles.
As i said before when you hear about axles the first you may think is about rigidity. Actually, the rigidity is the parameter taken from 2 other parameters, which are the outside axle diameter (first number, 30, 40 or 50) and wall thickness (50mm in many cases have 2mm thickness, 40mm have 3 and 30mm have 5..) So, the higher the diameter and the wall thickness the higher the rigidity of the axle and this make the axle very stiff and hard with high moment of inertia. What that means in practise? That actually means that a very hard axle, because of the high inertia, it won't tend to bend (don't forget that axles are actually working like torsion bars but in a different way) and when you are loading the rear of the track (when accelerating or turning) the axle doesn't want to absorb the pressure and all that pressure finally goes to the wheels. The more loading to the wheels, the more pressure to them and the more pressure the more they get hot! Now its clear that in cold days or in raining conditions we must use a stiffer axle in the rear (to raise the tire temps). If u go softer you actually let the axle to absorb an amount of the load taking place while the weight transfers to the back and now the wheels and tires taking less pressure than before. Less pressure means less traction and the tires tend to slide. Try move your finger on your desk once relaxed and then forcing it against the desk. Obviously in the first case your finger will slide better with less friction. The tires work about the same. Now we know why if we are looking to reduce the understeer we must use a softer axle. In a hot summer day i may use a softer axle. As the track gets more traction lap after lap (more rubber) i may go softer to let the tires slide better and gain more speed in the exits. Another parameter which in my opinion isn't so important to consider about is the length of the axle. Generally, the more length the more rigidity (keeping all the other parameters the same). Comparing two 50mm hard axles with the same wall thickness (2mm), the 1040mm length gives 769 rigidity while the 1000mm gives 740. So, to summarize, having two different axles but with the same rigidity will act about the same. For example, a 50 x 1,5 is approx. the same as 40 x 3,5. Which will be your final option? Well, it's up to you. The final two parameters (weight and material strength) must be taken into account before install the new axle in your kart. 

Info : a rental go kart uses a 25mm solid rear axle of near 5,5 kg weight..! Material strength in that case is important.

[high]

Hey all. I did some research on how the back axle on a go kart works and i would like to share it with you. In KRP there are seven different options to choose from and i'll make a try to explain the differences on them in the following sentences. First of all we must know that 'rigidity' is the key word behind the axles and this is the basic parameter of the axles. If an axle has high volumes of rigidity or in other words "moment of inertia" that makes this axle stiffer. This condition refers to a more stable back (more rear grip). You can say that the harder the axle (high rigidity) the kart tend to understeer. And vice versa the softer the rear axle the more oversteer. I don't want to say a lot so i will make a summary from 2 different sources from which i have put in perspective 4 different parameters, including outside diameter, wall thickness, rigidity and weight) of the different axles :

*  before you continue note that the numbers below are for comparison purposes mainly and they may be differ from real life. 

(rigidity min. 86 max 789)

axle diameter/ rigidity (hardness)/ weight
50 soft = 348 rigidity          (2,38kg)
50 medium = 435 rigidity    (3,28kg)
50 hard = 740 rigidity         (4,57kg)

40 soft = 240 rigidity          (1,89kg)
40 medium = 300 rigidity    (2,75kg)
40 hard = 511 rigidity         (3,57kg)

30 hard = 271 rigidity         (3,00kg)
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Remember that rigidity means hardness and hardness means more grip (understeer) so you can deside what axle to use in any case. For example, if you are currently using the 50mm hard axle and you feel that the kart has generall understeer your second choise must be 40mm hard. Going from 740 rigidity to 511 will propably fix your problem, if not then you may try the next option (50mm medium) with 435 rigidity. Note that the weight is an important parameter here - i dont know if KRP took it into account but in real life plays a huge role in seeking the 0.1 sec of your lap times. In generall, if 2 axles have about the same rigidity then the axle with the bigger diameter weight less. Just look above and compare the 30 hard with the 40 medium axle. The 40 M weights just 0,25kg less even though it has greater rigidity than the 30mm hard. So, your final axle choise will help you to fine tune your chassis and drop more your lap times. Hope this helps

Oversteer --> 40 soft --> 30 hard --> 40 medium --> 50 soft --> 50 medium --> 40 hard --> 50 hard --> Understeer