Honda Accord likes to feel a breeze under the hood

I have a 2000 Honda Accord EX Coupe with 160000 miles on it. Earlier this year I started having a problem with it when I would drive for long periods of time. When I would try to start her up, she has a very rough idle, then the engine just shuts off. I discovered that if I pop the hood, and allow the engine to breath for a short period she will start up just fine. Recently when she does finally start, she will idle very rough until I increase speed to over 30mph for a few minutes. She doesn’t do this everyday, but it seems like the problem may be getting worse. My mechanic is completely baffled, and aside from changing spark plugs and other minor attempts to solve the problem he has no idea what could be wrong. The problem seems to be somehow heat related, but the engine isn’t overheating. Once she cools off for a few, she starts up. Any suggestions on what could be wrong? Also I have started adding a fuel system cleaner to the fuel prior to fill up to see if it may help. I’ve only done this once so far.