How can I reheat oats in the minimal time without microwave?

No, I don't see how you can do better.

To heat something quickly, you need quick heat transfer. Water is the most efficient liquid in the kitchen to use for that, and its maximum temperature is 100 C. You're already using water -> oats heat transfer at its maximum speed.

If you were to use a liquid which can be heated to higher temperatures, you'd need to switch to oil. But then you'd be deep frying the oats, which is not only messy, but also changes the flavor a lot.

Then you could just try radiant heat + convection: an oven. But if you want the oven to work quicker than boiling water, you'll have to have a very hot oven, like a commercial pizza oven or an Aga, already running at full temperature before you stick the oats in. It's not practicable in most home settings.

There is one possibility: that you are already using the most efficient method available, but are using it wrong. I didn't understand exactly why you are adding extra water and then waiting for it to evaporate. Have you tried using less water and waiting for shorter time? Is it that your oats were cooked with too little water the first time, or parcooked to too early a stage, or what's the problem there?