Take notes! Play familiar stuff.
If you can position the secondary, or in question, amp close to the present main fav, the interim time frame will be shortened and should help. Naturaally too, if the 'B' amp is also on during the note taking on the main amp, the warm up time will be further shortened... However do connect a load to the 'just hanging out' amp while it's on.
Stepping outside for a few minutes too will help you refresh your ears... then go in and sit down to audition the other amp.
Those would be my thoughts, but the note taking is KEY.
Good luck.