where is the thermostat? 91 4afe

My girlfriend's 91 Celica ST had unusal highs and lows in her engine temp, so when I looked in the usual place (in my experience anyway) for the thermostat. it was not there. I'm talking about where the top radiator hose goes into the engine, I unbolted the 2 bolts, took it off, and it had a square housing inside the engine block, so I don't think the thermostat was previously removed. Maybe where the bottom hose connects?...I really don't know much about celica's, so any info would be nice.

Lower hose.....:eek:

thanks