solved.
Hi,
I think it is natural to get hot while playing intensive-CPU game. Especially for old computer. The exhaust fan maybe choked with dust or fan speed is reduced.
Just get a laptop stand with fan from Sim Lim and it will probably solve it.
I doubt the problem had anything to do with the CPU, replacing the thermal paste was not a good idea as it may have lead to this issue now.
As TrueSon says, it's likley dust in the venting that's causing the issues. If you open the lappy again and clean the fans and vents should help a lot. Also check the fans are all plugged in properly.