HR is good. But I’ve definitely seen big differences in HR between a certain wattage on the trainer and the same wattage in a hot country.
Another simpler tactic is breathing. Do long intervals on your smart trainer at the intensity you want to tackle the climbs. 10 minutes into an interval, what’s your breathing pattern? Once every 3 pedals, once every 4? Try to replicate that on the climbs and if it’s getting too difficult to breathe at that rate, slow it down a bit (or give it a bit more if you’re barely breathing at all).