I have a '93 Civic DX that runs great.  But for the past year it has been
driving me absolutely nuts with this hot staring problem.  It would start
right up in the morning, but running errands became a crapshoot...short
trips between stores almost always resulted in starting problems.  Also
parking in the sun might result in no start.

Do a Google search, something like "honda hot won't start"  If the main
relay is your problem, you'll see people describing the same symptoms
you've experienced.  

I finally found the same site Caroline listed:
http://www.markl.f9.co.uk/howto/electrical/main-relay/main-relay.htm

This was on thursday 6/24/04.  The amazing thing was that when I pulled
out the main relay  and looked at the soldering with a magnifying glass,
the *same* joint pictured on the web site was bad on my main relay!!! (It
*is* a pain to get the Main relay out; it's up under the dash near the
fuse box in my Civic).

If you can solder, the fix is easy.  I used copper de-soldering braid from
Radio Shack and a Radio Shack 30Watt soldering iron.

I let the iron heat up, then put the desoldering braid next to the joint
and pressed on it with the iron.  The solder melts and gets sucked up by
the braided copper. (I'll bet you could just strip some multistranded
copper wire and do the same thing)

I used some thin rosin core solder.  Just touch the hot iron on one side
of the component lead coming up through the circuit board, and touch the
solder to the other side.  As soon as the solder flows onto the pin, pull
the iron away.  The result should look like the other (good) joints on the
board.  I didn't redo every joint,only the 2 that looked marginal.  

Bottom line?  No problems since.  I spent all day today going from place
to place, starting and restarting with complete confidence.  I was parking
in the hot sun just for fun!!

Since it's intermitant, it's tough to diagnose.  Mechanics unfamiliar with
this problem either admit they're stumped or try to convince you they've
fixed it by doing something else.  If you are uncomfortable trying to fix
it yourself, make sure you let the garage know that you want them to test
the main relay before trying anything else.

Good luck!