The "correct part" stopped being manufactured a few decades ago. It's a thermostat with a flapper valve built into it that plugs off a large diameter bypass hose after the engine warms up. With a conventional thermostat, the bypass runs all the time, so there's no possibility of overheating during warmup, or at any other time. The big hose bypass system was only used on heavy duty vehicles like school buses or dump trucks. Unless the heater hoses are disconnected or there's a shutoff valve that completely stops flow through the heater core, there's a large volume circulating through the cooling system as soon as the engine is started. You're concerned about a problem that doesn't exist.
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
Love your enemies and drive 'em nuts!