Problems starting a 1999 Ford Taurus

We have a 1999 Ford Taurus with about 67,000 miles. Recently, we’ve had problems starting it. After we drive it for awhile, turn it off, and then try to restart it after about 15-20 minutes, it cranks up, but doesn’t turn over. We have to wait awhile (maybe an hour minimum) and then it starts. Of course, nothing registers on my mechanic’s computer and he can’t replicate the problem at his shop. He did experience something similar with a 2000 Taurus, so he replaced the PCM relays. Unfortunately, that hasn’t helped. Any suggestions?

Ignition module and crank position sensor are two things to check out.