The floor is also a normal temperature.

Sounds like floor heating. Heated Floors don't really feel warm. They just don't feel cold. From the temperature experience you are having, this sounds like the most likely case

I would have to guess that your apartment is being heated by radiating heat from other apartments (probably below you) as well as insulated by good quality walls and windows, and then this is supplemented by radiators when deemed necessary by some kind of sensor.

It's also possible you have underfloor heating if you live in a newer apartment in a country where that's common. But it wouldn't be my first assumption.

There is one radiator in the apartment's living room, at the front and down the hall from the bedrooms, and one radiator in the bathroom.

Depending how big is two bedrooms (In an era were there is cramped 40 m^2 3 bedroom, and huge 200 m^2 one bedroom loft) it's more than enough to heat-it.

Are you in a house or an apartment?

I'm on the fifth floor and pretty much never have to run my heat.

Maybe still floor heating? If the apartment is well insulated, the floor is only slightly warmer than the air, since the large area allows for heating with a small temperature difference.

It can be heat from surrounding units, especially those below you. Heat rises. There is a 15 degree difference between my upstairs and downstairs sometimes.

Are you sure it is?

Perhaps adjacent/lower apartments are heated and are leaking enough heat to you.

You are in the UK now so the chance of it being underfloor heating is very slim indeed unless you are in a new build from the last 5 - 10 years or so, even then I would doubt it though.

It is probably a combination of the amount of insulation we put in walls, floors and roof spaces along with the fact you downstairs neighbour or neighbours if there is a basement will be using theirs and obviously heat rises.

I know many people here that live in flats above other people that will never switch their heating on and live comfortably.

It is likely that those radiators are your only heat sources coupled with presumably a gas boiler to serve both the radiators and your hot water taps. There will be some kind of controls for it somewhere though, not all systems with have a thermostat in place. My current house has 3 radiators with no thermostat. It is either on or off or you can set time intervals for it to switch on and off by itself but there is no temperature based control.

British magic, specifically.

The water in a floor heating system is around 30 degrees celcius so it's not warm enough for you to necessarily be able to tell by feel. However bathroom would be the first room I'd imagine them including it on and the fact that there's a normal radiator there leads me to believe it's probably not floor heating. Ceiling heating is a thing too but quite uncommon.

It's probably just good insulation

Maybe an infrared heater somewhere? They can look like a painting or whatnot, while actually serving as a heater first and foremost.

It sounds like my old place. So long as you don't have a corner unit you're not being heated. You're being sheltered from the cold by the surrounding units. The baseboard heaters are only there to touch up if you crack a window or something.

Good insulation in walls and ceiling

Ambiently

I think the issue has s largely been explored and solved but I'd like to add something to the mix.

Complexes have hot water pipes running from the water heaters on the lowest floor up to all the suites. Usually they are stationed somewhere around the center of the main building, sandwiched between a commons hallway wall and an apartment wall.

The amount of heat that these can radiate is insane, especially if there's a hot water circulation system in the building.

Are you on the ground floor? If not then maybe whatever is below you is really warm and the heat is coming up through the floor. But I guess in that case the floor would feel warmer.

Checked the temperature of the ceiling?

Wait until summer. It'll become hell.

Something, somewhere, is on fire. The heat energy from that fire is variously converted, stored, transported all the way to your apartment. Once it arrives, it is converted back into heat energy. This is commonly accomplished by forcing electrical energy through a conductive filament.

The air in your apartment absorbs that energy, becoming "hot". When that air contacts your skin, transferring some heat energy to it, nerves inside your skin activate, sending a tiny electrochemical pulse to your brain.

That tiny pulse of energy bounces around patterns of interconnected neurons in your brain, forming a sensation of warmth, which is experienced consciously.

The nature of consciousness is left as an exercise for the reader.