Faster HR with heat suit on means more calories burned?

mcbadger there is much evidence to show that excercising in moderate to warm temperatures increases calorie burn - though less on excercise in extremely hot temperatures.

https://www.acefitness.org/education-and-resources/lifestyle/blog/1061/do-i-burn-more-calories-when-it-is-hot-outside-or-cold

The extra calorie burn comes from a variety of places and is not just restricted to the extra pumping of the heart muscle.

Thanks for the link. I've read it and the references with great interest, but they don't support your statement or answer my question - could you point me to anything else?
Specifically, the only comment in the article is "In hot weather, it takes more cardiovascular effort to COOL the body, which occurs by pumping blood to the skin to promote sweating. Therefore, exercising in warm weather would actually use more energy than exercising at a temperature near freezing" which is exactly about extra pumping of the heart muscle, and doesn't say anything about how much extra power is needed to support that.
The references mostly talk about changes in balance between burning fat and glycogen to support your power output, which is interesting, especially if burning fat is your target (though in terms of sustained weight loss, total calories burned is more important than where they come from in the short term). The closest they get to discussing power is showing oxygen used per minute (which is a fair surrogate for power given that calories generated per litre of O2 used are pretty similar for fat and glycogen) - in particular Figure 2 in Reference 2 shows oxygen consumption highest at 4C, dropping at 11C, further at 21C, and at 31C being very similar to 21C, but not sustainable for as long. They also conclude that fat metabolism is highest at 11C ambient and found that subjects sustained their workload longest at that temperature (probably a combination of using glycogen more slowly and taking longer for core temperature to reach the point where the subjects can't continue).

For Darkice2 , what I'd take from that is that working out at higher ambient temperatures isn't going to increase your calorie burn, but will reduce how long you can sustain that rate. If anything you might be burning off more fat at 11C ambient, but with your body fat percentage I really don't think you need to worry too much about that. I appreciate that's not very helpful to someone with OCD.

I think it would be useful for you to have a lab test so you will better understand how many calories you're burning. Both your resting and your maximum heart rates are quite low, and it may be that the algorithms are not ideal for your particular range. 30 calories per mile walking is pretty low at your weight, and 450 calories in an hour working hard is also surprisingly low (I would burn something like 800 in an hour running well outside my half marathon pace, and at 156 lb I'm heavier than you but not twice your weight :)

Beyond that the best advice I can give you is not to put yourself at risk trying to burn more calories, and I think that your heat suit workouts are putting you at risk for minimal gains. One other thing I got from the papers that JS referenced is that changes in ambient temperature, other than when it is very low indeed, only make a few percent difference in power output, and you can get the same effect by working out a little bit longer at a more comfortable temperature, and be able to sustain the same workload for longer at that temperature in any case. I've never used a stairmaster nor used cryotherapy and I'm not going to speculate about either of them - hope somebody who knows more can advise you.

Darkice2 I realise that you are focussed narrowly on one objective but I do thing that you need to think about the stresses that you are putting your body under. 6% body fat whilst it might give great muscle definition is below the threshold where a number of medical sources conclude that it may impact your health. Now many elite endurance athletes do have low body fat percentages (8% ish) but they have the benefit of constant medical oversight. Much lower than 8% and you have many potential health impacts - suggest that you read around. Aside from that major inputs of caffeine are not healthy for your body and combine that with the additional stress input of the heat suit and you are somewhat into uncharted territory. What is in your fat burner supplement ?

I agree with JSRUNNER_ here.
I don't believe the article you referenced, darkice; it's taking the calories from the Garmin at face value, and it's more likely that the caffeine is pushing up the subjects' heart rate without altering the calories burned doing those specific workouts, causing the Garmin to overread. Reading around, I found that caffeine might kick your base metabolic rate up a bit but it's about 150 calories/day, so trivial really. I suspect (but don't have evidence for it) that the main benefit of caffeine is helping you sustain a load longer, or a slightly higher load in the first place, and when you're working on your stairmaster at a set rate, the calories you burn are controlled by your efficiency and by the work rate of the settings, so none of the interventions you're trying are really going to make much difference at all.