i would say the fan...if it was the thermo it would happen all the time.

it sounds like its fine once it gets some airflow going to it. if there are two fans, which there usually are, the lower temp fan may not be working. but the higher temp fan might be thats why it has been getting close, but not there yet. should be able to get into the relay box and jumper it and find out pretty quickly, could be the fan itself, or a relay/fuse.