If you decrease the temperature, you slow down the atoms, and you decrease the gas pressure. You can't move one without affecting the other. This means that gas at the center must be very hot, over 10 million degrees hot. Since the outside of the Sun is much cooler than this, the heat at the center of the Sun must flow out. There are three ways in which heat can be transported.
Heat can move through convection.
This is the equivalent of taking the hot water of a bath tub and stirring it in with the cold water. By and large, this doesn't happen in the Sun either. The third method of heat transport is through radiation. The hot electrons at the center of the Sun radiate light. The photons travels a very short way before being absorbed, and the absorbing material gains the energy.