Well ladies and gentlemen I have a little trade secret that through personal experience can save you a bundle of money.
First - do not go to buy a new computer unless the one in question is a total piece of garbage.
Do not panic and buy some software program guaranteed as a quick fix.
First consider this method below and then if it doesn't do the trick, then be sure that you have defragged the drives, uncluttered and reduced the amount of items in the start menu, cleared cookies, temp files, etc.
Do both. The point here is to do what you can and not spend $$$.
I paid a repair place a nice chunk of money and waited several days to get mine back.
Meanwhile, I had gone out and bought a new one.
When the computer in question was finally fixed I went to get it, and the repairman told me that it was full of accumulated dust.
It had caused a thermal overload, therefore slowing down the computer more and more until it would shut down on its own due to the protection circuitry kicking in.
So here is how to take care of that.
First unplug the computer from the wall or just take off the electrical plug from the back of the computer and unplug the other stuff just in case.
Don't forget where it all goes.
I like to mark the places on the back for people who don't remember what plug is for what.
Then making sure to touch the case with your hand to discharge static electricity, lay it down on the floor or a table so that you can open the case and will easily access the innards.
Touch the case again from time to time to discharge the static.
Always be sure to discharge any static into the case so that it doesn't kill the sensitive electronics inside.
Now to clean there are several methods.
About the heat; I have a small room with no specific heater in it but the computers heat the room fine in winter.
Technicians use compressed air in a can.
You can buy it online or in the computer department of most stores. Be careful with that, as well.
The compressed air can be damaging for two reasons.
It can lift and move parts if used too closely, and the air used up close, (due to the venturi effect) can freeze hot components causing damage.
It would therefore, be better to clean the computer after it has cooled down.
The sudden difference in temperature can cause solder joints etc. to crack because it causes a quick, though unnoticeable expansion and contraction of materials.
So after, you have done that. Fire it up and hope that the dust was the issue after all.
Otherwise, take it to a repair shop or use it as a doorstop.