I just happened to have an OE Crossfire thermostat in the garage.

It comes already fitted into the aluminum housing. Yo see here the two "wings" on the thermostat which slot into these grooves on the housing. It's a secure pressure-fit between here and the second round stamping on the thermostat which seats into the housing...

...which you see here.

Inside the housing the pintle of the thermostat fits into this nipple-extension. I couldn't photograph at an angle which lets you appreciate the length of these pieces inside the housing.
I'm sure a machine fit the thermostat into the housing but ask yourself, "Is a machine more capable than you are?" :-)