While ideally a piano would be kept in some special room with controlled humidity and temperature, that's rarely possible. For many of us in small houses, finding Any space big enough is a challenge and often walls that are not used for furniture have inconvenient radiators on them.
I would assume that putting a piano right in front of a wall with a radiator would be a terrible thing to do to it - but what about being a couple of feet away?
You can use heat reflecting panels between radiator and piano to have some protection. This helps radiator to heat only the circulating air but not the surfaces it sees directly.
Also place a bowl of water with a wide surface (for better evaporation) under the piano and over the radiator to increase humidity during heating season.
A couple of feet is as close as you want to be. It depends also on how hot that rad gets, and how long it's on for daily. One of mine is about 3 feet away, but because it has an iron frame, it's not been a problem. Wooden framed pianos can get dehydrated causing all sorts of nasties.
"...walls that are not used for furniture have inconvenient radiators on them." So put the furniture over the radiator instead!
'Too close' is the distance at which heat from the radiator causes noticable warming of the piano. You're not really going to be able to space the piano far enough out. Put it where there isn't a radiator. Sorry.
I have a century old piano that has been sadly deformed by a 1 foot away radiator, the wood buckled causing the metal back board to crack on three horizontal points, this would cost a couple of grand to put back right, and since I have no where else in our living room, I am thinking of buying an electric piano, in hope that it would not face a similar fate. The problem with those is that they are much smaller than acoustic pianos and would never look right in that corner of the room, besides their sound and feel to the touch would never be like a live acoustic instrument.
