Engine Performance
Air becomes thinner as altitude increases. Altimeters take advantage of this, using air pressure as a proxy for measuring height.
Air becomes thinner as temperature increases. This is because the kinetic energy of the molecules increases, pushing them further apart.
Engine Performance
A model aircraft engine (non-electric) burns fuel to create energy. The more fuel it burns, the more energy it creates. "Power" is the measure of the "rate" of energy production. An engine that produces energy more quickly is therefore more powerful. Power is limited by the rate at which the engine can burn fuel. Fuel needs oxygen to burn. The limiting factor is not the amount of fuel that can be squeezed into the engine; it is the amount of oxygen that can be squeezed in. Denser (thicker) air has more oxygen per cubic centimeter. Therefore low altitude and low temperature produce the most power.