Fire Genasi do not really tolerate low temperatures better than humans, and while they are "feverishly hot" it is not a game mechanic like an Azer's Heated Body feature. However Fire Genasi are able to cast the Produce Flame cantrip at will, and the Burning Hands spell once per long rest.
Fire Genasi do not have resistance (let alone immunity) to cold damage, so they are the same as humans in that regard. Resistance means the creature takes half damage from cold damage, and immunity means the creature would take no damage from cold damage (barring very special circumstances/spells that could negate such resistance or immunity).
However, all Genasi including Fire Genasi do get a +2 bonus that either goes to Constitution automatically or can be applied to Constitution if using Tasha's Cauldron of Everything ("TCoE") optional rules in Chapter 1 of that rule book.
The benefit of a higher constitution score is laid out in Dungeons Master's Guide ("DMG") pg110:
EXTREME COLD: Whenever the temperature is at or below 0 degrees
Fahrenheit, a creature exposed to the cold must succeed on a DC 10
Constitution saving throw at the end of each hour or gain one level of
exhaustion. Creatures with resistance or immunity to cold damage
automatically succeed on the saving throw, as do creatures wearing
cold weather gear (thick coats, gloves, and the like) and creatures
naturally adapted to cold climates.
(The rules regarding Exhaustion can be found in the Player's Handbook ("PHB") on pg 291 where it details the effects of exhaustion, which can be quite serious up to and including death.)
Accordingly, depending on how much you put towards your Fire Genasi's Constitution score, it could make a little difference if for some reason you were caught in the cold without proper clothing.
As an aside, the Goliath player character race found in Volo's Guide to Monsters ("VGtM") rule book was always adapted to cold climates so it would always succeed on its saving throws vs extreme cold, and it has further been updated (in what is called an errata) that now gives the Goliath resistance to cold damage, a very substantial benefit.
Even further aside, Xanathar's Guide to Everything ("XGtE") rule book includes a racial feat available only to Tieflings called Infernal Constitution which among other things gives resistance to cold damage.
As to the body giving off heat, Fire Genasi are only feverishly hot, unlike an Azer's Heated Body feature, described in Monster Manual ("MM" rule book) pg 22 which states:
Heated Body: A creature that touches an Azer or hits it with a melee
attack while within 5 feet of it takes 5 (1d10) damage.
Accordingly, a Fire Genasis being "feverishly hot" is good for flavor, but there is no game mechanic advantage say compared to a human.
Finally, Fire Genasi do have the Reach to the Blaze racial feat, allowing them to cast the Produce Flame cantrip at will, and the Burning Hands spell once per long rest.
The Produce Flame cantrip does not appear to aid with cold damage or exhaustion from exposure to cold. Rather it provide illumination and can cause damage to other creatures.
On the other hand, the Burning Hands spell outlined in PHB pg 220 includes the following in its description:
The fire ignites any flammable objects in the area that aren't being
worn or carried.
Accordingly, this could help start a fire in the event you are caught out in the cold without proper clothing, and have access to fuel for a fire. However, a Tinderbox which costs 5 SP and weighs 1 pound would likely accomplish the same thing (refer to PHB pg 153).