The short answer for swordtails
Yes, in practice — with a small asterisk for warm houses. Swordtails have a reputation as indestructible beginner fish, and relative to many species they are forgiving, but they are tropical livebearers at heart and their comfortable range runs from about 72 to 82 degrees Fahrenheit. A tank in a genuinely warm, steady room might hold the low end of that range unheated in summer. The trouble is the rest of the year: cold nights, winter drafts, and air-conditioned rooms drag an unheated tank below the range again and again, and it is that repeated sagging, more than any single cold day, that wears swordtails down. A heater removes the question entirely.
River fish from Mexico and Central America
Wild swordtails live in rivers and streams from Mexico down through Central America, in water that stays warm year-round and often moves briskly. They are built for that life — active, social surface-and-midwater fish that graze algae, chase each other through plants, and breed with an enthusiasm that has made them a hobby staple for generations. Breeding is the key word for the temperature question: a swordtail colony in warm water produces regular batches of fry and the females stay in good condition doing it, while a colony kept at the chilly edge of its range breeds sporadically, drops weaker fry, and leaves females depleted. If you keep swordtails, you are almost certainly keeping a breeding colony whether you planned to or not, so their water should be set for breeding, not mere survival.
Heating the swordtail tank
Set the heater for the mid-70s Fahrenheit — comfortably inside the range, with margin on both sides — and verify it on a thermometer placed away from the heater. Install it during the cycle so the tank's temperature pattern is proven before the first fish, and recheck the reading when the seasons turn, since a tank that held steady in September can sag in January. Fry change the heating picture slightly: newborn swordtails collect near the surface and in plants, so make sure warmth reaches the whole water column, which a heater placed in the filter's flow accomplishes better than one tucked in a still corner. If the swordtails share the tank with other livebearers or community fish, the mid-70s setting will suit nearly all of them at once.
What cool water does to a swordtail colony
The signs arrive as a pattern rather than an emergency. Breeding slows or stops. Growth in young fish stalls. Individuals that used to patrol the surface start hanging in the plants, fins a little clamped, and the colony becomes prone to the white spots and fungal fuzz that healthy warm swordtails shrug off. Check the thermometer early in that pattern — a drifting heater explains more mystery colony declines than almost anything else. Restore warmth gradually, and if fish keep falling ill in water that reads correctly, or females keep losing condition after giving birth, that is the point to take the colony's history to a veterinarian who treats fish or a knowledgeable aquatics shop. A breeding colony generates a lot of shared jobs in a household, and the relatives you pick can view their profile through Family Sharing in KinsLe, once you have given them access to it, before checking the tank.