What temperature home do bunnies like best?

The temperature in our living room where our 8 mos. old mini rex resides is constantly changing. At night, I usually shut the heat off so it goes down (we live in a building so it never gets that cold but its not warm). Then, when we wake up, the heat goes on. Sometimes I leave it on during the day and sometimes I leave it off. I know bunnies shed during the summer and grow fur in the winter but I feel like my home is a mixture of summer and winter and his shedding habits may be slightly confused.

Any thoughts?

Give him towels/blankets to keep warm and tiles or frozen water bottles to stay cool. The rabbit should be able to keep his body temperature stable if you provide objects to help.

Since the temperature is changing not too rapidly, it shouldn't be a problem, healthwise. It could mess up their shedding, but so what, rabbits are fine at temperatures we find acceptable indoors in winter. I heat with wood, and don't heat every day when I'm too busy, so the room temperature is between 8°C and 20°C (they prefer lower temperatures), and my rabbits can go out in the garden during daytime too. Dotty sheds right now, Herr Hase not. So what, doesn't matter.

Indoor rabbits have crazy shed cycles. Just the way it is. If you are comfortable in the house then they will be just fine, especially if it's on the cooler side.

Our house gets quite warm even with A/C in the summer. When our outside temps are hovering around 115F, we struggle to keep the house between 80-85F. That's when I'll put a frozen water bottle in the cage (they already have cool tile on their floor).

I keep my house around 66-70F in the winter, and both my rabbits seem to like spending time next to the front door, back sliding door, or flopped against a wall that faces outside. I get the impression that my rabbits find the room temperature in here a bit warm and seek out colder spots in the house.

I've heard that 55 is the ideal temperature for (adult) rabbits. They are cold-weather animals; I wouldn't worry about it getting too cold for them. Making sure you don't heat it up too quickly when the heat turns on in the morning would be more of a concern for me, imo.