Howdy and welcome!
I believe what you're terming "voltage regulator" is more aptly termed "voltage limiter" as it limits the voltage to the gauges to something like 5.5 volts, rather than a full 12 volts.
Look at the factory wiring schematic to see where the voltage "feeds" for those two circuits are. It's possible they are fed from the same source. Provided that the related grounds for each circuit are good, finding the issue with the voltage feed could well fix the issue. It could well be a wiring issue behind the instrument cluster down to the fuse block.
The temp gauge should be a "direct" wire, I suspect? I suspect you have already checked that wire between the temp sensor on the engine to the bulkhead connector and then to the gauge itself? I san "sensor" as "sensors" vary voltage to the gauge as "switches" are for warning lights, although both are classed as "senders".
Everything depends upon "grounds" being good and solid. Any added resistance in those connections can result in skewed readings of the respective gauge.
It seems that many people get in trouble trying to wire around factory wiring as it might seem to make sense to them to do so. Just use the existing architecture and put it back to "as produced" configuration. That's usually the best way to do it, in the long run. There might be a few exceptions to that rule, but they can be few and far between, by observation.
There are later model voltage limiters which are solid state rather than "vibrating points". They were used on '80s Chryslers, I believe, as OEM. I believe you can find some in replacement vendor sources, too.
Just some thoughts,
CBODY67