My car has had the same problem for a few years but I was able to manage it until today.
Previously, if I forgot to crack the windows and sunroof on a hot summer day, the cab would get REALLY hot and my car would not start. No click, no starter, just no noise when I turned the ignition over. I also noticed over the past few years that my "engine work" light would not turn on when the ignition was turned. Normally all the dash lights light up and I noticed the engine maintenance light would not turn on.

I was able to manage this problem for years by simply remembering to crack my windows and sunroof. It would still happen a few times each summer but all I had to do was open the doors and get a crossbreeze going. After about 10 minutes, car would start no problems.

This last sunday I forgot to crack the windows and it was a sunny day. After waiting for a half hour with the doors open it still wouldn't start. I tried later at night when it was nice and cool and the car still wouldn't start.

Any ideas? Could this be a relay starter problem?

 

Refer to the troubleshooting flowchart in this link:

Honda Acura ignition (no spark) troubleshooting tutorial - How to

 

Almost a classic Main Relay issue......check the post by Redbull-1 but that is where my money is at