That's a fundamental asymmetry.
Maybe it's also the reason why body core temperature is close to environment maximum temperature - since you can't really decrease your temperature you might as well learn to live at the upper extreme.
I wonder how much of the species' worldwide dominance can be attributed to the evolutionary diceroll that placed our ancestors in subsaharan Africa? Could we have survived in Egypt, Mesopotamia, or India without sweat?
Sweating works well in dry climates, not as well in humid ones. In high enough humidity, the sweat doesn't evaporate, doesn't cool you, and the whole system becomes a moist, messy loop.
In dry, hot climates sweating works well, but increases our water consumption... these are the habitats where water is often scarce.
Tradeoffs.
I know sweating isn't perfect, for the reasons you mentioned, but do we see nature evolving any better solutions at a mammalian level?
My armchair understanding is sweating is a natural marvel with nothing else like it seen in creatures as large as us. That it truly is a differentiator between humans and other animals (or mammals at least). Sweating is the foundation of humans ability to engage in long-distance endurance running which is one of our unique features, also called persistence hunting[0]. You can easily draw a line between this sweating and our ability to travel large distances and hunt the way we did, which in turn can be connected to humanity's success as a species on earth.
African wild dogs, dingos and other canines can persistent hunt in similar hot conditions. They're much faster than us, so it's not as extreme a strategy as human "track and spook" methods... but arguably better.
Elephants manage to carry those huge, heat retaining bodies. Our Savannah nurseries are full of megafauna like us that live in these conditions effectively.
Some argue sweating, others that we outsourced digestion (fire cooked food), others that we are bipedal, ... not to mention later stuff like language/intelligence.
Also, cats and dogs do sweat a little, mostly through their paws.
I don't know about the other part (temperature/pressure).
There is a MinuteEarth video about this YouTube if I remember correctly and the reason is well.. more reasonable. Our body works better at higher temperature, but of course if it gets too high everything breaks down. So the optimum temp is somewhere closer to the upper limit.
You can adjust the gradient so as to change the rate of heat loss, you can grow fur, shunt blood flow away from outer surfaces - or the reverse. Humans have clothes and even buildings to do this even more. Say you're losing 10K per hour and producing 5K per hour, if you cut the gradient to 50% you break even and your temperature remains viable indefinitely.
But that only works when you're losing heat. If you can't lose heat, this doesn't help. You will die.
Heat naturally flows from hot to cold at a rate proportional to the difference in temperature. If we're fully passively cooled at an environmental temperature 25°C at a rate of 2°C/day, then at 1°C, we'd be passively cooled at 6°C/day. However, we can also modulate heat flow by introducing some thermally nonconductive layers--or, in layman's terms, put on a sweater. When it's cold, all you have to do is slow down the rate of heat flow.
But hotter temps are more difficult. We can't take off thermal insulators or modulate the main thermal barrier between core body temperature and the outside world (i.e., skin). At 31°C, passive cooling is down to 1°C/day, and we need to turn to active cooling. Sweating is the main mechanism for humans: it takes heat for liquid water to become water vapor, and this heat is drawn from your skin surface, cooling it (this kind of allows heat to move from a colder to a hotter environment, unlike passive cooling). At 37°C, there's no longer any passive cooling, and active cooling needs to handle 2°C/day.
But hotter than that, and things get worse: the environment is now passively warming you up. By 43°C, that's now 3°C/day of heat that needs to shed, and 49°C ups it to 4°C/day. At some point, you're going to overwhelm the ability of active cooling to cool you down, and the passive heating is still going to warm you up even if you shut down metabolism. Even worse is if sweating isn't effective at cooling down--at high humidities, the sweat won't evaporate and the cooling effect won't happen. (This also illustrates why heat-and-humidity can be deadly even at below-body-temperature environments.)
This analysis was purely done for humans, but it's pretty similar for most organisms, just with different set points for core body temperature and active cooling mechanisms. Fundamentally, extreme cold is "easy" to handle--just slow down heat loss; extreme heat requires developing ways of pumping heat from a hot reservoir to a cold reservoir, which thermodynamics does not look kindly on.
But you can't take off your skin to sleep on a very hot night.
All in all I would say the temperature tolerance is the same in both directions.
https://www.ancientpages.com/2016/09/19/mystery-yaghan-peopl...
Meanwhile, life at cold temperatures goes on. A lot of animals can adapt to a temperate 0C-20C conditions, and colder. Humans adapted and thrived, like many/most megafauna to pretty cold conditions. The far north has been inhabited by people for half a million years. You can get a lot further from comfort and still make it in the cold.
Heat is deadly.