Two things, first let's address the possible heat issue (I do not feel that this is a heat issue.)
your computer may be experiencing some overheating due to dust buildup. Can you open the side of the case and inspect the fan(s), air intake vents (front, back and sometimes side) and the processor's heatsink?
A few pictures of heatsinks in the following links.http://www.google.co...l=en&q=heatsinkhttp://en.wikipedia.org/wiki/Heat_sink
The heatsink fins will often become compacted with dust, and the fan blades will aquire buildup as well, all of which prevents good air flow and resulting cooling of the processor. The power supply (where the power cord plugs into the back of the computer) also has a fan and air flow vents, both of which can become clogged with dust. Overheating of either or both the power supply and processor can cause the computer to shutdown as you've described.
The best way to remove the dust buildup is with compressed air, which is available in cans from most any general merchandise store, office supply store and electronics store if you don't have access to an air compressor. When using compressed air to clean, don't allow the air flow to spin the fan blades. Hold the ones you can and use a toothpick or similar to hold the ones you can't get to, like the power supply fan (back of the machine).
Do NOT use a vacuum cleaner to remove dust. It can create static electricity which might arc to your computer's components thereby damaging it.
Second (I believe that this is the issue) your hard drive may be corrupted to the point that you can not complete the recovery proccedure. (the drive may be failing and as it is used the heat causes issues, or the sectors are so corrupt that they can not be written to)
Do you have the ability to install a new hard drive? If not I will give you some links to articles that will give you step by step instructions.UNPLUG the power cord before opening the computer case!!!
(It is not enough to just turn off the computer, It takes 2 seconds to unplug the computer and reduce any risk of electricusion!)Use the same kind of hard drive EG: SATA to SATA and ATA (pata) to ATA.
The recovery disc will stall if you use a different kind of hardware other than what was used by the manufacture.
An article on installing a new hard drive can be found by clicking this link http://www.fonerbooks.com/r_hard.htm