My 1988 honda civic is sometimes hard to start when hot. After cooling down for 1/2 hour or so, it will then start. What's happening?

Test/replace the igniter and coil. AutoZone will test these components for free.

I am 99% positive this is your Main Relay dying. Which happens to be a chronic problem for older Hondas in hot weather. Check out the follow website:

<< Main Relay Fix, Troubleshooting (Honda, Acura) and how to solder >>

I had the same problem about one week ago. Performed this fix as laid out above and was cured one hundred percent. Good luck.

- Drew :)

Check out that site mentioned in the earlier post and if you need another way to verify if the car won't start than tap it like I did and then it started so I knew it was the problem.