At a low temperature gas molecules travel, on the average, at slower speeds than they travel at a high temperature. So, at a low temperature the molecules have, on the average, less kinetic energy than they do at a high temperature. Lower speeds, lower kinetic energies.
Temperature, when measured in Kelvin degrees, is a number that is directly proportional to the average kinetic energy of the molecules in a substance. So, when the molecules of a substance have a small average kinetic energy, then the temperature of the substance is low.
In the following animation gas molecules are modeled as little circles. They are bouncing around in a sealed container.
This animation shows all of the molecules of a gas traveling at the same speed. This is not a perfect representation of their motion. Actually, these gas molecules would all travel at different speeds. However, for any temperature there is an average kinetic energy and a corresponding average speed of molecular motion. This and the following animation move all of the molecules at this average speed.
Below is a simulation of gas molecules at a higher temperature than those shown above. Compare them carefully, their speed is not much greater, but is in fact greater. These are faster by a factor of the square root of two, 1.414. This makes the average kinetic energy of these molecules to be twice that of those above, since the kinetic energy of a body is proportional to the square of the speed of the body. Consequently, this lower animation represents a gas at twice the Kelvin temperature than the gas above.
The area of this animation is twice as large as the area above so that the pressure of the gas is properly simulated as being equal to the pressure above. This allows us to properly see the effect of a temperature change on the speed of gas molecules without concerns about other effects due to pressure changes.
What you should notice in this lower animation is that the higher temperature is tied to a higher average speed. This results in the molecules having a higher average kinetic energy.
In the bottom diagram there is an increase in the kinetic energies of the molecules due to an increase in heat.
Heat, as stated earlier, is energy. If the kinetic energies of the molecules go up, then the heat has gone up. Therefore, in the example which we have examined here, an increase in heat has caused an increase in temperature because the increase in heat has been realized as an increase in the kinetic energies of the gas molecules. When the average kinetic energy of the gas molecules goes up, the temperature goes up.
An increase in heat is not always accompanied by an increase in temperature, however. That is very important to understand. The heat (energy) could be used to change the bonding between the molecules rather than be used to speed up the molecules. This would be a situation where heat goes into a substance, and the temperature does not rise, as when ice melts or water boils. In these cases the increase in heat (energy) is used to change bonding between the molecules rather than change their kinetic energies.