When an ideal gas is compressed adiabatically, its temperature rises: the molecules on the average have more kinetic energy than before. The kinetic energy increases,

The gas is ideal and the collisions of the molecules are elastic. When the molecules collide with the moving parts of the wall, its kinetic energy increases but the total kinetic energy of the system will remain conserved. When the gas is compressed adiabatically, the total work done on the gas increases, thereby kinetic energy of gas molecules is increased as the internal energy of gas increases and hence, the collisions between molecules also increases.