To heat only one side of a rotating sphere involves a minor heat source orbiting in a nearly geo-stationary orbit … a micro-sun orbiting over the east hemisphere. The micro-sun would need to advance slowly around the globe to move the ‘seasons’ east-west, otherwise one hemisphere gets perpetual summer and the other perpetual winter.
Which is basically what I had in mind with the brown dwarf/star combination. The whole point is to have one hemisphere in perpetual "summer" and the other in "winter".

At first, I was thinking this might be a fairly common type of planet in the galaxy. Hoping there might even be a known star system with suitable parameters, I found this instead:
https://en.wikipedia.org/wiki/Brown-dwarf_desert
Brown dwarfs are rare in close orbits around stars. The exceptions are where the star is a red dwarf.
That is, systems where the same planet could receive significant heating from both are unlikely.