Mechanical oil temp gauges are readily available, any racer supply or almost any gauge supplier. They are virtually identical to the water temperature gauge (not oil pressure), except perhaps for having a somewhat higher range. So just like the temp gauge, they have a bulb that has to be exposed to the oil; and a armored "capillary" tube that runs from the bulb to the gauge.
ISTR the Stag head temp sensor mounted on the back of the head, but I don't recall which head offhand. Dad's 455 Buick had two of them, one for each head and they were on the back. (That model engine had a bad habit of developing air bubbles in the heads that would allow them to overheat even when the radiator was full.) Unfortunately the TR head doesn't have a lot of extra tapped holes and no good place that I can think of offhand to add one. Maybe if you could find a sensor that would screw into the plug for the cam oil feed?
When they rebuilt "Uncle Jack" (a Stag that was restored for charity), they literally found not only sand, but a casting core, still buried in one of the block passages! Somewhere there is a photo of Joe pulling out the core, but I don't have the link handy.
But I will say that the TR3 motor is very tough (at least part of the reason we sometimes call it a TRactor motor) and at least in my experience rarely suffers any damage from overheating. I now believe that pretty much all of the head gasket problems I've ever had with a TR motor can be traced to inadequate liner protrusion.