You could put the thermostat behind the door.

I put the light switch, fan and GFCI outlet in triple gang box in my old bathroom.

You can do a GFCI outlet/switch combo with a separate fan timer, or a fan timer/light switch combo with a separate GFCI outlet. That gets you down to a double instead of a triple or quad. You can put the thermostat on the other side of the wall (outside the bathroom). You can even put it in a remote place like a closet. That assumes it's only sensing the floor temperature and not also the air temperature. You can put towels on the back of the door.

Badgergal put a nice hand towel stand on her new vanity in her remodel. It goes between the two sinks, and has a towel on each side. I really liked it for practicality and it also looks very nice.

Unfortunately, those stands only hold fingertip towels, not hand towels. I have looked all over for for ones that would hold hand towels and have had no luck.

I'd want the light switch to be at the "standard switch height" for your house. That way there is no searching the wall for the switch in the darkness. Or out of habit.

I'd not want the towel hanging on the ring/bar to cover anything up.

Nor would I want the wire from whatever is plugged into the outlet to be in the way of any switch or to get tangled with the towel. Will things be permanently plugged into it? Or will it be "time of use" only? That can make a difference.

With the Thermostat most likely being the least used and if it can't be set at the same height as the light switch, I'd set that a bit higher up on the wall than the light switch/fan switch combo, but aligned vertically with it.

Personally, I prefer fan/light combo timer switches. A single switch controls both. You turn the switch on, the light and the fan come on. You turn the switch off, the light turns off immediately but the fan runs for an additional preset time.

If you did that, you could put your fan/light switch and outlet in a dual gang box at the appropriate switch height. Put the thermostat in its own single-gang box a little higher on the wall, but aligned vertically with the switch box.

Below that, at a height high enough to keep your draped hand towels off the countertop (if I understand your situation I think it's hand towels), but low enough to deconflict with the outlet, place the towel bar/ring.

I'd use painters tape and mock up the locations and see how they work. Unless I'm really misunderstanding your description, I don't think "how they look" will be an issue. "New things" sometimes look weird to the un-used to it eyeball. Once you get used to the look, all will be well. So prioritize substance or functionality over style.

We have our full size hand towel in a rectangular, metal holder originally made for guest paper towels, on the countertop. I fold it in half lengthwise, then roll it up and place on holder. Working great for 8+ years. Just an idea.