Came from fall Los Angeles to Cozumel in 2016, so did some of that. You say no sauna but I think that was the most helpful TBH, Was harder than I thought it would be so started about 3 or 4 weeks out (can't recall exactly but there is a time frame where it is most beneficial). Started with 2X short sessions and slowly increased from there

I did a few easier trainer workouts with no fan and long sleeve shirt That was fucking miserable and left my shoes wet for days. Can't imagine adding a heater to that. I'd emphasize no hard sessions like that.