The Promise Mechanic is really stupid in some cases.

I promised to keep all homes warm. But because the weather turned slightly colder i instantly was given the broken promise thingy. I didnt even have a chance to turn the heat up further. Its just instant. Give me atleast an ingame hour or something when something suddenly change so i dont just instantly fail.

Same if the weather got warmer i wanted to see if i could turn down the heat and BAM. I broke promise. Thank you. I werent going to break it. But try to save on coal if i could...

This one is a bit nasty, as it's often outright impossible to succeed on the task if there's an impending cold snap. Due to the timing of these kinds of requests, you're often aware of the cold home problem and already intended to do something about it, so you just reflexively agree to the promise without noting the weather forecast. Before accepting this one it's important to check the forecast, and if you see a temperature drop you should be very cautious about accepting. If you see a two-stage drop, just forget about it!

In this case i could manage it fine if the game didnt just instant fail you when this hits or if you wanna test out of lower heat is still good enough to save coal

I can understand this being frustrating the first time around, but there are warning symbols on the calendar, so you actually have several DAYS of warning that the temperature is going to drop.

You have to pay attention to it - the game even slows down at 5:00 - one hour before the cold hits.

Try read exactly what im saying.