By definition an adiabatic change is one in which no heat energy enters or leaves the system of interest. Doing work on a gas (by compression) or having it do work (eg push a piston) results in energy entering or leaving the system (but not heat energy as such). If the system is in thermal contact with the outside the temperature change accompanying the work will result i heat entering or leaving until temperatures are equal. This would be an isothermal change. If the system is insulated (or the change happens so fast that heat cannot flow to an appreciable extent, eg sound waves or even convection in the atmosphere to a great extent), then the change is adiabatic and the temperature of the system will change and not equalise.
From memory, the pressure/volume law for the gas is different in the two cases, PV =constant for isothermal and PV^gamma =constant for adiabatic.
This should put you off the subject for good....
Pressure-Volume Diagrams - The Physics Hypertextbook