Won't Start

Hi, I've got a question about a Honda Civic. This is my girlfirend's sister's car, so I don't know the mileage, engine size or year, pre-2000 I do know for sure, but hold with me for a sec., it's a pretty vauge question that could probably happen with many types of Civics.
Her Civic will not start when it is hot outside (above 90 degrees F). The car will crank, the electronics will operate completely, but it just won't turn over. What will make it eventually turn over is if she opens the hood to let air circulate around the engine for about 20-30 minutes. She has taken it to mechanics and they have tested everything they could but found nothing wrong with anything. Finally one mechanic told her that it is a problem with the car's computer where the heat under the hood is not allowing the computer to give the engine the proper pressure needed to turn over. The problem is always fixed by opening up the hood and letting air circulate around the engine for a while. Is there anything this girl can do to fix this problem short of spending wads of cash on new computer equipment, or really, a new car? Does the computer theory hold water? Thanks to any one who dares answer this one.