The main concern with running without a thermostat isn't overheating, although the dwell time of the coolant in the radiator could be an issue. All engines are designed so the parts establish a correct running clearance at a particular temperature, and the 350 is designed to run around 200 degrees or hotter. I can usually spot an engine that's been run without a thermostat when I tear it down for a rebuild by looking for a thin shiny area in the middle of the piston skirt. An engine that has been run at the right temp will have a much wider piston-to-cylinder contact patch because the piston heats up and gets round at the proper operating temp. Bearing clearances also get right when the crankshaft and rods run at the correct temperature, and the rings expand to minimize blowby.
Jerry
