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

because of collisions with moving parts of the wall only

• The elastic collisions of the molecules with a moving part of the systems increases their energy.
• When the gas is compressed adiabatically, the total work done on the gas increases its internal energy which in turn increases the KE of gas molecules and hence, the collisions between molecules also increase.