Well sir I don't know your level of tech expertise and without writing a book I can explain it like this - if you open the computer case there will be a large aluminum thing with cooling fins and a fan perched on it. If you can see how to remove it (some have clips and some have screws so its hard to say what you should do here) you just take it off exposing the processor chip. You then apply some thermal paste such as Artic Silver that you get from any run of the mill computer store to the top of the processor chip and then replace the heatsink on top of it. Sounds like you have an older computer so the original paste that was there might be kinda dried up and the move may have made the heatsink move so its not making optimal contact with the chip. Oh also don't pull it off unless you already have the new paste already to reinstall.
If you were closer to me I would offer to come take a look at it... Perhaps if you posted a pic of the inside of the pc we could walk you
through it lol
Have you tried an application such as Speedfan to check or monitor your temperatures?