I may not be reading this right, but it sounds like you are currently running your computer with either ZERO thermal paste or with Dried Thermal Paste.... if either one is the case then do this:
TURN IT OFF!!!
While your computer may run a few hours and seem fine or even a few days - it will sooner or later fry and possibly damage your entire system - irreparably. I made that mistake once when I was first learning these things and I fried a $350 mobo.... don't make my mistake - wait until the new thermal paste arrives... and be sure to clean the old stuff off well.

Good luck and have fun.