Although... now that I think about it... I suppose it might be possible to add overheating as a secondary mechanic buried in the options menu. I'd have to increase the normal bullet damage when it's active to compensate for the fact that the player would be firing fewer shots per minute on average, but in theory there's no reason why it couldn't be totally self-balancing... hmmm...
For example, if 50% downtime is necessary to prevent an overheat, then normal shot damage needs to be doubled for the rest of the gameplay to stay the same... Yeah, that might be generalizable, if I can get the math right.
And of course there would be a bar or a radial indicator or something. The problem with "stamina bars" isn't the bar. It's the stamina.