Temperatures look ok so far.
Core2Duo CPUs -besides being very energy efficient- have a built-in overheating protection.
If they ever reach high core temperatures, the frequency is decreased. If the temperatures get critical the CPU powers itself down.
Chipsets usually get a bit hot when under load.
80°C is still about 25 degrees below critical.
Which graphics card do you have ?
Afaik the power supply in these machines has only about 360 watts which is not enough for some high power graphics cards. This is very likely the reason why your PC freezed. Gaming video cards not only consume some watts, they also generate a huge amount of heat when under load.
Anyway, there are two things you can do:
First, go to HP Support and get the dc 7800 manual.
Uninstall the processor heatsink and apply new thermal paste (don't forget to clean off the old one).
Then, increase the idle fan speed in F10 BIOS Setup for better airflow.
