They don't do much if they're swamped with towels, though they are useful for drying those towels.
Ours was broken for months (blocked pipe apparently). I can't say it affected the temperature of the bathroom much. Soggy towels though. It's one of those radiators with multiple bits for hanging towels, not just a singular rail. Technical terms r us.
If I did the bathroom again, I'd contemplate underfloor heating, but to be honest as we can (and most) leave the bathroom door open it's typically at the ambient temperature of the rest of the house, and upstairs is usually quite toasty. Plus there's three radiators directly below the bathroom (one in the hallway, one at the bottom of the stairs, and one in the downstairs loo), so I think we get underfloor heating by proxy.
Of course, if I lived in a cold house, it might be different.
(I'd always assumed Mumsnet was some kind of niche porn site. I'm somewhat disappointed that it's towel rails.)