If it’s any comfort, I had several months of frequent thermal sensations and extra sensitivity to heat (from about month 5-8 keto) - and for me it correlated with a lot of fat burning as well as nourished brainz. And it passed - it’s gotten much easier now. But I empathize, as the excess heat can feel claustrophic, and one’s mind can get agitated about it.
You mentioned being 5 months in and having ‘yet to lose a pound.’ I wonder, are you measuring yourself? Ketosis is about fat burning & lean mass restoration and recomposition, not necessarily about some idea of body mass weight. Some gals may have no weight change - but lose sizes in clothing and have much leaner bodies, etc. You may well find proof of some wondrous changes happening that way and it can be really encouraging, as for non-obese females who are rebuilding lean mass & connective tissue, the scale may be maddening. Personally I avoid the scale at all costs, because of the psychological issues some of my family members have had with their weight on the scale.
I was amazed when during a 6 week period recently I had 1.5 inches disappear from EACH of my upper legs! For women, there are also fat stores on our backs and lower bellies specifically related to cortisol levels over the years. Keto combined with good stress management and/or certain supplements can unlock those areas and expedite lots of ch ch ch CHANGES.
A goddes-send for the short term could be to get you some personal air coolers - the “Arctic Chill” small swamp cooler fan box chills the air in a 2-3 metre area away from where you are sitting or laying (it doesn’t chill entire rooms, just your personal space). It lowers the temperature good 10 degrees fahrenheit, and the chill is very nice. A similar device helped me SO MUCH when undergoing thermal flushes (which are quite different than hot flashes, when one compares the symptoms) while working at my desk with warm computer, etc. They’re available on Amazon for forty bucks or so these days. I currently have one on my desk, and one on my nightstand.
It’s also possible that you have co-arising thermal flushes + hot flashes + night sweats - and a heckuva a lot of metabolic healing and/or detox going on. The LCHF/keto way of eating will no doubt speed and support your processes.
Other help can be found in having a nice spritzer bottle of rose water or cucumber water or lavender water - I love spraying in on my brow and the top of my head and back of neck, very soothing. There was a time when I was spritizing myself several times in the afternoon/evening. Also, of course, making a point to cool your insides by enjoying one avocado a day, and/or fresh coconut or coriander/cilantro added to your meals - as well as certain kinds of keto treats like frozen coconut milk or dairy cream with berries & erythritol, etc. Another self-care remedy is to keep ice cubes in your freezer ready for moments when you need help - and then grab a small bowl or towel (to catch the drips) and one icecube. If you sit and hold the ice cube in your palm, it will distract you with a nice chill and also begin to hurt if you hold it long enough. You can practice breathing into and through the sensations, it’s sort like travelling to a high snowy alpine place. It can be quite distracting from the heat, lol, and the ice melts so it’s a limited time only anyway 
. Still, perhaps I’m on my way (towards metabolic health) and just need to be patient.
. I’ve been supplementing iodine as we never eat fish and live a million miles from the ocean. Perhaps I wasn’t low after all… (puts bottle back in cupboard).
I’d trade your 38 deg C days for one of my 40+ days though, hot and dry here 
.
Air Conditioning all the way for me! Stuff the greens they don’t have to pay our electricity prices!