99 Passat Warm Weather starting problem

My wife has a 99 Passat that has problems starting once the temp outside rises above 60 degrees F. She can turn on the key and all the lights turn on but no engine cranking. If she turns off the key and turns it back on sometimes it starts right up. Some times it takes several tries. Once the temp out side cools down to below 60 degrees or if the car is warm after running it starts just fine. We live in a cold winter area and it never has a problem during the winter months but once it starts warming up it starts doing this all over again. We've taken it to a couple of places and spent hundreds of dollars trying to isolate the problem with no luck. Any suggestions would be most helpful.