Hello, the apt we are soon moving into has radiant (heated) hardwood floors. I don't have any experience with this type of flooring.
Are there any restrictions on putting a rug down on the heated floor or a rug liner underneath the rug on the floor? Is there a special rug liner I would need? Is there a chance I could ruin the floor if I put a rug down on this type of flooring?
Some heavy carpets do not need any "anti slip" liner at all. If you are putting furniture on it, then it won't move. If you need anti slip, check that it is suited to underfloor heating. Is the hardwood sealed? We once had a problem with residue that was left on a wood floor from anti slip and it would not come off. The store where we bought the anti slip inspected the floors and paid for their repair. They said they were going to take the issue up with their supplier. It is not easy to clean under a carpet that has antislip so I would recommend not using it unless absolutely necessary.
When I first moved here, my husband had an apartment with underfloor heating. I never knew it, as you couldn't feel it because he had wall to wall carpeting with padding underneath. I thought only the bathroom had it, as that's the only place I ever felt warm.
When we moved out, the carpet and padding came up fine, though.
The last people in our place had rugs and the floor needed sanding after they left. The sunlight darkened the wood floor around the rug and left a noticeable colour difference.
OP did ask if they would ruin this type of flooring with a rug. I have heated hardwood floors and they were ruined from rugs, but from sunlight not from the under floor heating.
Anti slip mats are not only for anti slip but they protect the rug as they cushion the underside when you walk on them. Obviously not needed for all rugs, that decision is yours alone to make but anti slip mats are not expensive.
MarieZug has raised a really good point. When you cover the floor with carpet, you may notice changes in colour. I have seen this when someone had no drapes, not even sheers, to cut some of the light.
The last people in our place had sheer net curtains, just that it gets full sun most of the day. I can live with dints and scratches (having a little boy means every inch has dents now) but the discoloration looked really bad. Why anyone would want to cover a nice, easy to clean wood floor when you have underfloor heating is beyond me.
I think with young children a rug is more comfortable to play on than a wood floor. But we also already have the rugs before we got the apt otherwise I would have thought twice.
Rugs also help reduce the noise, something families with children in apartments worry about. In previous houses we had laminate flooring and marble, which were both very slippery but when we moved now that we have all ceramic tiles, we sold all the carpets. The noise level is completely different. I also found it is not easy to clean around/under area rugs. They do look nice though.
We use a carpet play mat with a white rubber backing that I can wash. Anything with black rubber seems to leave yellow marks, eg bottom of coffee table legs and speaker bottoms. This could be caused by the underfloor heat heating the rubber. So, a dark coloured rug liner may leave these marks.