- We know, that sometimes galaxies "colide" (not like car crash, but like two flocks of birds flying different directions)
- There were many natural nuclear reactors on Earth burning for many millenia (or even much longer)
- not all stars are equal, not all planets are equal
So have some two galaxies cross its ways, that just some solar systems on borders get somehow "near" each other to the effect, that they heavily interact with each other. And one planet was as an effect slingshoted by gravitations forces somewhere else (while other planets was just messed up or something).
Let this planet just dull burn out piece or rock, flying interstelar space for milenia and totally cold, until it hit other younger solar system (from that coliding galaxies) in very lucky way - it was traveling really near the Sun, got slingshot from it to lose a lot of inertia and got catched in that solar system as a strange comete.
Then it hit one of local planets, roughtly its own size, not fully colded, which made them merge and make new planet, where the cold one is one half, the hot one is other half (more a huge layer over half of the cold one) while at the connection was formed big ring many times higher, then Kilimanjaro around the whole planet. Also the impact change its orbital trace to more better one. (and destroyed everything on both parts, but we are forming planet now, life will came much later anyway)
Now we have planet in the right distance of (relatively weak) Sun, which is rotating and everything, but one its half is old dead rock, other is hot radioactive young planet, both parts are separated by mountain ring about atmosfere hight or at least much higher, then freezing water line, so the air does not mix much.
Over time it stabilize somehow, get continents, oceans and later even life, at least on the radioactive side, which is warmer, as it actively produce heat (and lose it to space), while the other side just get heated from the other part via masive, more then half planet huge mass of badly conducting rock) and lose that heat to space too. There is some snow, so it also reflects heat from sun much more, that the happy half.
The life here is accustomed to higher radioactivity and many vulcanos around, as it developed in this conditions. (Yes, we have a lot of natural radioactivity in background too, and there are organismus on Earth, who are even much more resistent to extensive radioactivity, so why not).
The local Sun provides a lot of energy, but not all needed. The younger part of planet provides also lot of energy, not as much as Sun, but enought to sum to pleasant climate. The older part does not, so it is arctic regardles its position.
We do not lose watter, as it rains and snows on the ring-hills on winter and on summer it flows back to oceans on warm side. There may be some caves thru the hills, maybe there are some Himalayan ways too, but there is not much of such ways, so not substantial watter and heat is lost or transferred to the cold side. But it may be possible to climb there and use some of the few ways to get onto the "other side" for motivated people - like it was to get to Kilimanjaro or to the poles on Earth. Hard to do, but possible, but only on few places, which are not so big, to change the climate substantially.
Depends on your plan, how bad is the cold side, but there may be also some life (vegetable or even animal), or at least there could be human stations, as the cold side may contain some valuable resources, like minerals.
Practically it is two different planets, with the same gravity and ecliptic, with some connections usable for humans, but otherwise with totally different clima and resources and lifeforms (more different, than rabits here, platypus in Australia and penguines in Antarctica)