|First look up your beep code.|
If you removed the CPU heat sink or even just loosened the lock downs and shifted it even a minute amount then you will absolutely need to remove the thermal paste and reapply new thermal compound properly.
Proper methods for applying thermal compound:
How you proceed depends on a few factors:
Did you get the beeps first and the overheating later after you did the cleaning (possibly improperly)? If so then after properly resetting the heat sink and addressing the beep warning, you MAY be fine (post back results and for additional advice).
Did you get the overheating issue first and then the beep warning only after the cleaning (possibly damaged another component or left something unplugged or reversed position)?
HOW did you clean out the dust (compressed air [good], vacuum [not good], brush(metallic or non-metallic) [not good, metallic much worse], etc)? Did you remove components when cleaning? Did you remove any connectors? Did you move or remove or vacuum off any jumpers (small plug like pieces without any wires on them)? Were you aggressive in moving around wires? Did you ground yourself before touching anything internal?
Answering ALL of these questions that apply AND supplying your system information (make,model or component list) is essential to evaluating the problem.
You have to be a little bit crazy to keep you from going insane.