That rules out a faulty transformer....

I dont believe there is any kind of heat sensor in those lamps.

Sometimes electrical equipment can become naturally sensitive to heat and you may have a bad solder connection in the light housing.

Check all connections and I would try to elliminate the GFCI as a source just in case. The last resort would be to replace the light housing.

Since it happens every time it should be fairly easy to narrow down the source.