Dense rings and a tight orbit around a cold star
The planet is in a tight orbit around its tiny, coldish, host star - "years" are a few hours, (the "24 hour day" is actually a beat in the day / year rhythms.)
The planet also has an extremely thick ring system, and as the planet goes through a "year" in a few hours, with axial tilt, it goes through summer and winter every few hours. The rings shadow keep the higher northern latitudes cold for half the "year", and the lower southern latitudes cold for half the "year".
The end result is 2 sharp lines of latitude where the total amount of daylight is halved (the sun rises and sets behind the rings every few hours).
The close orbit makes things blindingly hot along the equator. And there's a tiny temperate zone straddling the two.
The planet is a little outside of the suns habitable zone, just a little too cold. A resourceful race comes along and notices a valuable ore in deep deposits below the frozen equator. Rather than tunnel hundreds of shafts through 10km of frozen solid planet, they decide to make the ice go away. So they build orbiting mirrors in geostationary orbit to reflect extra sun onto the planet, focusing on the equator, as that's where they want to mine first.
And then, nothing. The project was cancelled. The mirrors are still there, blasting heat around the equator onto the frozen planet.
The end result is big polar frozen regions stretching a long way, a big desert region around the equator where the mirrors have over melted, and a tiny habitable zone straddling the two
Shiny, elliptical moons
If aliens are a hard no, a bit more of a stretch but don't involve aliens, we can replace the mirrors with shiny, metallic moons.
A number of highly reflective moons In equatorial orbit could reflect light onto the equator at night time. The moons are slightly elliptical so the light is distributed more over the equator than the rest of the planet, making it very hot. Otherwise the setup is same as terraforming aliens.
Active volcanoes at the poles keep the sky outside of the tropics covered in an ash cloud, resulting in year round freezing temperatures.
The hot sun keeps the equator very hot. There's a tiny zone just under the edge of the ash clouds where the sun doesn't boil you, and you don't freeze. Except for the epic sunsets, the ash is too thin to see with the naked eye.