2002 Saturn L200 problems starting after short stop

We purchased a used 2002 Saturn L200 in December. It has been running
great all winter. The weather has recently been getting into the upper
60's and twice within the past week my wife has had problems starting
the car after a short stop.

The first time was when she stopped to get gas. It wouldn't start so I
drove over to the station. She had been trying to start it on my way
there with no luck. I tried too ... it sounded like it was making a
half-hearted attempt to start but nothing. After letting it set a
little we were going to push it over to the side but I decided to try
one more time. It started right away!

The next time she went to drop something off at church. She shut off
the car, went inside for a few minutes then when she tried to start it
again it wouldn't start. When she called me I said to try letting it
sit for 10 minutes and try it again. It started this time.

Do these "symptoms" suggest any thing? Are there some simple things I
can check? Oddly I just ordered the "Haynes Saturn L-Series Repair
Manual 2000-2004" the day before the first problem. Hope it arrives
soon!

Thanks
Rich