No. There is no reason to be watch an oil temp gauge.
The heat in a harley is not in the oil it is in the heads and exhaust. The heads are not oil cooler except on one engine.
Oil cooler is nice to have but not the end of the world if you do not have it.
Put a HD cooler and in fairing temp gage on my ultra almost as soon as i got it. At first, i thought something was wrong with the gage till i brought out the thermometer and verified that the oil was barely getting to 180. It was only about 60F outside, and the thermostat was working properly, as the cooler was not heating up either. Figured that since i plan on slowly doing some mods that it would pay off eventually. Well, was in Oklahoma in August and got caught in traffic, I know they only work when you are moving, but i was moving intermittently and the oil got up to 260. One thing i do wonder about, when i was in that traffic jam and it was getting hot, the pressure gage showed almost nothing till you were at about 1700 rpm and that kind of worried me a bit.
I use an analogue dipstick in my softail however my temperatures stay low as it never gets hot here although on occasions on summer trips we have encountered hot weather oil temp has never been above 220 Brian
If you have not done so, I suggest opening up the nose cone (cam cover) and checking the tensioner shoes. Your engine has the spring loaded tensioners with their inherent problems. If they are worn, or getting close, consider up-grading. If not ready to do that, and the shoes are still greater than 50% beef, consider replacing the pressure relief plunger spring with the Baisley LMR-002 Spring. This will increase the oil pressure by 10-15%. See here:
Baisley Hi-Performance Oil Spring Product
Roller Chain Conversion White Paper
Roller-chain Conversion - Harley Davidson Community
TQs Engine Build
TQ's Engine Build - Harley Davidson Community
TQ