Front and Rear roll stiffnesses

[riff_raff]

How fast a tire carcass heats up is due to how much energy is transferred into its body mass.

A radial ply tire has less rolling resistance than an older bias ply tire, so the radial would naturally heat up less (all other things being equal) than the bias ply tire. A tire with a soft rubber tread compound would have higher hysteresis losses than a harder compound tire, so it would heat up faster. And a tire with low inflation pressure would have a higher rolling resistance than the same tire with a higher inflation pressure, so it would too heat up faster.

Lots of variables to consider.