A bathroom mat is at the same temperature as the tile. However, the tile makes your feet cold faster because of higher thermal conductivity.

Assuming you don’t plug in your bathroom mat to turn on an internal heater, the mat is the same temperature as the tile floor. Everything in the room is at about the same temperature: room temperature. The tiles conduct heat much better than the fluffy mat, which means they suck heat out of your feet much faster. This is not just a psychological effect. Your feet actually get colder on the tiles. But it’s because of high thermal conductivity, not low temperature. Granite tiles have a thermal conductivity that is 100-150 times higher than that of cotton bathroom mats, according to The Engineering Toolbox. That means your warm feet loose heat 100 times faster to the room-temperature tiles than to the room-temperature mat. The sensation of cold you experience is your feet at a reduced temperature due to rapid heat loss, not the tiles at a reduced temperature. Three of the best thermal conductors are diamond (which looses heat 1 million times faster than cotton), gold (11,000 times faster than cotton), and copper (14,000 times faster than cotton). So think twice before lining your bathroom floor with diamond, gold, or copper and throwing out the mat.