Yes, the TR4 sender fits fine (I have one in my TR3).
Another alternative might be to just buy a cheap mechanical temp gauge. I don't know if the electrical ones come with the same thread; but every mechanical gauge I've seen uses the same fitting as TR3; even when the package says otherwise!
Sorry, I have absolutely no idea of what the application was. But years ago, I was trying to get a TR3 home by driving it; when the Tstat housing fell apart. I carried the remains into a nearby FLAPS and scouted through the water outlets until I found one with the same bolt spacing. Of course not the same size & shape, and no room for a thermostat (or bypass fitting); but by adding a long flexible hose, it worked for 1500 miles or so. ISTR I used a sparkplug & hose clamp to close off the bypass hose.