The premiere enzyme responsible for fixation of dinitrogen to ammonia, the nitrogenase, is extremely sensitive to the presence of oxygen because of the degradative tendencies of oxygen towards the Fe-S co-factor of the enzyme. However, hot springs provide an ideal environment for diazotrophs or symbionts as the excess temperature ensures that the partial pressure of gaseous oxygen would be higher than the ambient atmosphere and generally results in outgasing of oxygen into the atmosphere and the water becomes hypoxic. This in effect is absolutely conducive for the nitrogenase to function. However, the temperature might prove to be a hindrance for the enzyme to perform optimally for which hot spring cyanobacteria or other microbes tend to synthesize excessive extracellular mucopolypeptides and other polymers. The dissolved carbonates in the alkaline hot springs serve as buffers to any pH swing, thereby protecting the enzyme.
At or near deep sea vents, nitrogen fixers encounter environments where the element with highest electron affinity is usually sulfur. And the absolute absence of free or dissolved oxygen in there immediate environments enable the nitrogen fixers to perform optimally. Production of methane, hydrogen sulfide, sulfur di-oxides farther bolster the situation of hypoxia. There are articles indicating that gaseous nitrogen is abundant in hydrothermal fluids and the environment itself is limited by fixed nitrogen. Hence thermophilic nitrogen fixers reduce N2 to ammonia in the unsedimented deep-sea vent regions.
In very cold regions, like the polar climates, the nitrogen fixation do take place beneath the ice or permafrost, in peat bogs etc but at very slow rates. And in it very rare in arctic oceans since the cold ensures presence of excess dissolved oxygen in the water which is a big roadblock for the nitrogenase. The global nitrogen cycle is not balanced since in the arctic regions, nitrogen fixation hardly, if ever, occurs, apart from some limited coastal settings and the rate of microbial denitrification far outweighs the ammonification in high latitudes. The tropical regions are characterized by higher rates of nitrogen fixation within the euphotic depth followed by greater ammonia oxidation through Annamox in the lower reaches of the nitricline.
This is why if all the niches of the world were considered, nitrogen fixation concept would have been needed to be rewritten as a result of a paradigm shift. Hence, in terrestrial conditions nitrogen fixation may or may not occur in polar climates but in water it is truly a rarefied phenomenon and can only, theoretically/hypothetically take place in oxygen minima zones, which needs rigorous research works/brain pooling to corroborate.
Microorganisms survive in a range environments depending on their growth requirements. If such N-fixing organism is thermophilic or hyper-thermophillic, of course it with survive and perform its metabolic activities in hot or extremely hot environments.