A lot of people want both underfloor heating and carpets. It is quite an easy effect to achieve - many of us may have first enjoyed underfloor heating in carpeted hotel rooms. The question arises then, what kind of carpet pad for radiant heat floor works best?
The answer to this depends on what type of radiant floor heating system you choose to go with. If you go radiant floor heat with electric power then all you need to worry about is choosing a system specifically designed for carpeted rooms. This is usually thin heating elements placed in a aluminum laminated roll. All you do is place it on top of the padding, under the carpet. Clearly in this case the carpet pad is not affecting the heating, so you do not need to worry.
On the other hand if you have a hydronic radiant floor heating system, the carpet pad matters. This is because these systems are placed in the floor - either set into the concrete or the floor joists. Clearly in this case if you place a huge thick pad between the floor and your feet it will act like an insulator, and make the floor heat less efficient.
This is not to say that you cannot use a carpet pad - what you need to find is a balance between heat efficiency and the comfort of a soft-treading, sound-deadening carpet pad. If you want to use the hydronic underfloor for cooling as well however, then you will need to do without carpet altogether or the cooling effect will be unnoticeable.