XRAY - Model racing cars

First thing I can think is : but what kind of shore did you choose ?
Second is: this is why normally before the start you have five minutes in warming up ...
Third is: did you make the correct diameter giving 1° of pre-camber to your tyres?

Not the whole times a hard rim is good, 'cause the foam consumption could became a problem ...

Some rims are made to be flexible to gain grip. I can imagine the heat of the tire and the forces on the rim must have some time to make the rim flexible.

Pre-heat the rims with a hairdryer to see if that will work.

What you say it sounds not so strange to me .
I called a very friend of mine, Dino Giacalone 7th in final, asking to him what a kind of problem he had during qualification phases.
He said he had a lot of trouble because the shore on the box weren't right, as where 42 was printed those tyres were 48! when they realised this, they tested ALL THE TYRES they have to find out a really pair of 40 front and rear (he run RRR) with a durometer and not the lie on the packs ...

Could be the diff oil heating up?