I agree with Hagberg and Big Jimmy G.
Primarily tires overheat because of friction forces inside the rubber itself. To prevent overheating two things need to be addressed: (1) dissipate excess heat, (2) prevent too much internal friction in the rubber from occuring.
The first point is relatively easy to address. If allowed enlargen the air holes in the wheel rim to let more air in and out of the tire. The airflow through the tyre will dissipate the heat. Moreover running a larger air gap will allow more air to directly flow past the tire dissipating heat even faster.
The second point takes a bit more work. The key here is to "dampen" the internal forces that build up in the rubber and also try to reduce the maximum force applied. The latter is something you achieve if you allow more chassis roll. If combine more chassis roll with more damping (slowing the chassis roll) you also reduce the maximum force applied. The extra airgap will help too as it allows the rubber to move a little before taking up the full force applied during cornering.
The last piece of the puzzle should now be obvious, softer inserts will also help to keep the tire temperature down.
All this does have negative effects too though. Harder inserts (and less air gap) will allow faster cornering assuming the car keeps traction that way and the tires don't overheat. The same is true for running less chassis roll. Thicker damping slows the transition which on tighter tracks is usually not something that would improve laptimes.
So the trick is to find the right balance. This depends on your driving style, the tires, the track surface, the track layout and the track temperature.
Did I scare you guys yet?