Just wanted to log a note for anyone with this problem.
My M6805 was shutting down out of the blue.
The fan would speed up and up then the machine powers down.
The interval of runtime got shorter and shorter.
I took my computer apart with help from:
http://repair4laptop.org/disassembly_emachines.html
It's not as hard as they describe and I didn't need any of the tools.
I used a rubber band to get enough friction to lift the hinge covers.

I took apart the heat sink.
It comes out fairly easily.
There is a piece of heavy tape going into the air intake for the
processor that looks questionable.
It holds the display cable in place and perhaps grounds it also.
Remove that tape.
Disconnect the little black ground wire to the lower right heat sink
screw.
The screws look large and have a funny top on them. They hold springs
that provide pressure to the CPU. Remove them, remove the fan cables
from the board and slide the thing out.
I blew it clean with 30 psi from a compressor with a fine point blowing
tool. Lots of dust came out. The fans make a pretty cool sound when you
clean them.
Upon reassembly I have no problem with the power down and the fan never
hits its max flow.
I did not use any paste on the interface. It was dry when I opened it
and just cleaned it with a little rubbing alcohol and a cotton swab
before placing it back down.
I did not put the orange heavy tape back in and gave the display cable
a bend to get it away from the inlet. So far I have no display problem
so it may not be relevant as a ground point.

This verifies that the problem is an overheating problem contrary to
some information out on the net.

-Tim