When I disassemble an engine for a rebuild, I an usually tell by the wear pattern on the pistons whether or not it has been running a thermostat. Pistons aren't round- - - -they're "cam ground" with the biggest diameter 90 degrees from the wrist pin. 45 degrees from the pin hole, they're several thousandths smaller. They get round as they reach operating temperature due to anti-expansion struts cast into the piston when it's manufactured. Engines that don't get up to normal operating temp regularly will have a shiny spot about 3/4" wide in the center of the piston skirts that's been carrying all the load, and varnish built up on the rest of the skirt where it hasn't been making contact with the cylinder walls. The cylinders will be worn egg-shaped, also. Running an engine with a too-cold thermostat or none at all is pretty foolish.
Jerry