+1 on the missing/stuck thermostat - these engines commonly get coolant leaks and the PO might have removed the thermostat entirely, or used a low-temp 80degC one. You could be losing pressure off the rad cap too.
It's good that you have heat...at least coolant is flowing around and you know the pump isn't air-locked. The M42 is a PITA to bleed, especially if the little passage in the thermostat housing gets plugged up with silicone make-a-gasket (don't ask how I know). BMW doesn't use jiggle valves like many other (lesser) cars do. My car takes a while to heat up nicely, and even then the hoses aren't really hot...just warm.
As for the gauge...when you swapped the motor, did you make sure the plugs were right? All three share the same two-pin plug type. I accidentally plugged my oil sensor into the DME temp sender after I did the hose delete mod. The oil pressure light was on (but dim) and the temp sensor didn't seem to work. Gave me some high blood pressure there for a bit. Swapped them around and all was better.