Has anyone driven with spare tire? It was a weird experience.

Here is my story: flat rear tire with a long nail through the sidewall (Wth?). Fortunately, tires are toward end of their life and i have a set of replacement tires. I drove some on a spare tire inflated to 55+PSI (my tire gauge goes to 55) and immediately noticed a difference: car not rolling freely and more effort on moving from stop. MPG in city was about 40, instead of expected 50+. Then I drove to my usual tire place and something weird happened: sluggish acceleration, no battery assist and ICE was on all the time while 'idling", just like with overheated battery, but the battery fan was working at the usual speed, barely audible over road noise. Again 40MPG.

Then coming back with new tires, no unusual hybrid action, except for mushy handling (new tires and lower PSI than I prefer).

What was that? It was a hot day, 90F+, but not unusual this time of year.

 

A donut in rear. No problems with the car whatsoever. About 100,000 miles. HV bat. warranty near expiration though.

 

I was not aware of that feature. What is the threshold for that disconnection for ambient temp? It was up to 95F on that day.
No dash lights.

 

No bisco, car sat in shade, it was driven in 90-95F for several miles, but problem with no battery assist started as soon as turned on. In retrospect, I should have restarted the car before hitting the street.
Also, the HV fan was almost silent, unlike one time long time ago battery was overheated due to spirited driving and then parked in sun. From then on I'm religious about parking in shade.

 

I will do it next time I get a flat. THX!