Why would temp gauge move up while driving then cause the AC to blow warm?

2006 Toyota Sienna XLE - Temp gauge moves up about half-way between
normal and hot while driving and causes the AC to start blowing warmer air
(compressor went off?).  Then at some time later (doesn't seem to be any
consistent trigger) the temp gauge goes back to normal and AC starts
blowing normal again.  Repeats somewhat randomly but is worst when
ambient temp is hotter (don't really notice the problem when outdoor temp in
70s but today it was 84 and issue was pretty bad.  Had the AC system
replaced last year and it seemed to fix AC (mostly - but also had cooling
system issues last year - thought we fixed).  Since the temp is high now, the
issue is very prevalent.  This also happens when I'm in a drive through or at
a light - temp goes up, AC blows warm until I get going - it's kind of random
when AC comes back on.