Heat is distributed in a fluid by convection. As the fluid near the heat source warms up it expands, gets less dense, and rises. The rising fluid is replaced by cooler fluid, which in turn warms and rises. As the rising warm fluid moves away from the heat source it cools down, becomes denser, and descends. Eventually, a convection current is set up. In this animation, the heat source is an electric heating coil that glows red (in middle of space). Licence a still from this convection graphic.
Like air being heated in a house, the heater causes an updraft, and the warm air spreads in all directions just below the ceiling, before falling at the far walls. Notice how there is also a random movement of the air as well as the circular bulk flow in the convection currents, all of which helps the heat to spread around the room. In real room heaters, a fan is often used to help spread the heat (fan forced convection). The same principle is at work in fan forced convection ovens.