You could try a different brand of ammo (as well as trying 130gr vs 150gr), which in many guns can make a big difference in accuracy. That made a difference with my .270 WIN (Tika T3 Lite, which also has a short, thin barrel).
The thin barrel is going to get hot, period. It's a thin barrel.
You can take the Texan out of Texas, but you can't take Texas out of the Texan.