So all the Todoroki children are cold-resistant to a certain degree, right? But except for Shoto none of them are particularly resistant to heat (and as far as I have understood it's more Shotoās quirks balancing out his body temperature than actual heat resistance the way Endeavor had envisioned it).
First, Iām going to assume that the power of the quirk itself (Fire/Ice) and the temperature durability (Cold/Heat resistance) are inherited separately from each other since 2/4 children have fire powers, but 4/4 have cold resistance so it doesnāt match up. (Or it could be polygenic inheritance, meaning many genes = one trait but that would be too complicated to get into rn)
Now, we know that in inheritance there is usually one trait that is dominant and one that is recessive, but if that was the case here, then ALL children would have the exact same power and temperature endurance level. Since that obviously isnāt the case it makes more sense for quirks in general to have incomplete dominance, also called intermediate inheritance which happens when both traits are equally dominant, so it results in a mixture (eg. White flower + Red flower = Pink flower). This in general seems more logical when looking at quirk pedigrees where the child's quirk is usually a mix of both the parent's quirks.
But even in that case, why did only one child get heat durability? Why didnāt all children get both quirks and/or both temperature endurances or at least a 50/50 mix of everything?
I think there are two reasons for this:
The first one is this: The quirks and temperature endurances work against each other. Because of that it is impossible to have both quirks at the same time. Ā Shoto evades this problem by separating the quirks from each other onto different body halves, so even though it is technically one quirk, neither side has to actually directly interact with the other. It is also stated that Touya's sensitivity to heat is BECAUSE of his cold endurance, so one canāt have both temperature endurances at the same time (again this is also true for Shoto where both halves have different endurances for different temperatures).
The second reason is even more essential though: Rei has an ice quirk and from what I gathered her core temperature is colder and if she uses her quirk it cools down her body even more (to the point of frostbite if she overdoes it). Hereās the kicker: Fetal temperature is maternally dependent until birth (usually it's supposed to be about half a degree higher than the mother's temperature), so they are supposed to be warm!
There are of course not a lot of studies on fetal hypothermia (too low body temperature) because usually they are pretty cozy in the womb and itās kinda hard to get the embryos/fetus temperature from in there but I think we can make some educated guesses, if we look at data from newborns, especially premature babies. For every 1°C decrease in temperature <36.5°C, the risk of death increased by 28%. Conditions of newborns with hypothermia : impairing growth, loss of brain function, organ failure, increased likelihood for more severe early respiratory distress, hypoxia, impaired fluid balance, hypoglycemia, hyperkalemia, fetal bradycardia, an accumulation of toxic metabolic by-products that may not be compatible with life, massive pulmonary hemorrhage in the absence of infection, impaired kidney function, late onset sepsis, inability to maintain their pH and developed a more pronounced metabolic acidosis
So those are all fully-developed newborns. Imagine the damage such cold would do to a fetus/embryo. So hereās my thesis: Itās not that the Todorokis genetics are funky: any child that didnāt have cold endurance (and by our previous logic NO heat durability) would not survive even the first couple of months of pregnancy or would be severely disabled (but to be honest I think the conditions are way to hostile for a pregnancy to be carried to term in that case).
On a darker note, if you go a bit further with this entire theory that means Rei must have had quite a lot of miscarriages to have 4 children in the end. Keep in mind that most miscarriages take place before the 12th week of pregnancy so a lot of times mothers donāt even know they are miscarrying/were pregnant in the first place.
So yeah, that might be the reason why the quirks in the Todoroki family are distributed so unevenly.
Thanks for coming to my TED talk.