Let's establish two things first.
Sound is a form of energy.
Waves are made by the oscillation (up, down and sideways movement) of partials. When partials oscillate, they transfer energy by bumping into each other.
Sound wave are waves that are created by the oscillation of air particles and carry sound energy from point A to point B.
In a warm room, the air particles have higher energy compared to a cold room. Hence, they bump into each other more frequently.
This allow them to transfer the sound energy quickly and easily from one partial to another.
Hence, sound travels faster in warm room then in cold room.