Geo, I don't believe any TR3s ever came from the factory with electric temp gauges, even TR3Bs made after the start of TR4 production. Lots of eBay sellers advertise something other than what they actually have (one of them assured me that the disc rotors he was selling were the original size for my TR2!) But the early TR4 electric gauges do look VERY similar, and were a popular conversion even then.
Also worth noting that while the TR4 gauges certainly do need a stabilizer; there were gauges of similar (if not identical) appearance that did NOT need a stabilizer. These were 'balanced' movements, similar to the TR3 fuel gauge; and sold as aftermarket accessories for cars not originally equipped with temp gauges. I have one somewhere, still in it's original display carton.
Anyway, in response to the original question, Yes, it's very doable. The TR4 sender will screw right in where the TR3 sender was, no adapter needed. The stabilizer does need to be grounded, but the original type stabilizers do not care about polarity so you can keep positive ground if you want.
The aftermarket electronic ones do care about polarity though, so if you go electronic, be sure to get one that matches your setup.