Is the part number on the thermostat itself, the same one on the parts list? I've had wrong parts shipped in "right" boxes before.
Be careful about the manual restricting--consider that to be a "get me home" patch. There's still something WRONG and no telling what other damage it may do (now or at some future point) if you don't track it down and correct it.
I think every cooling system thread eventually comes down to the same line: You need to put eyes and hands on the entire cooling system, from intake to exhaust, and follow through every inch of it. Someone, somewhere, may have added in a hot water heater (incorrectly rereouting plumbing) or tapped a line, or SOMEthing, and sadly there's only one way to find out what and where: Go spelunking.<G>