The contrail from the tail wasn't necessarily created by the APU. It might have been a vortex generated contrail like we often see them from wing tips in humid air.
Last Thursday, even if we had temperatures in the 70'es, the air was very humid. I watched a satellite photo of the country on the weather bureau web, and even if the cloud cover was scarce, then the whole country was practically covered with high altitude airliner contrails.
Often the contrails evaporate in minutes, but last Thursday they staid for hours and became thousands of feet wide.
Always keep your number of landings equal to your number of take-offs