We present a diode pumped, electro-optically q-switched Tm:YAG laser with a cryogenically cooled laser crystal at 120\,K. Output pulses with up to 2.55\,mJ and 650\,ns length were demonstrated in an actively Q-switched configuration with a repetition rate of 1\,Hz. By using cavity dumping the pulse duration was shortened to 18\,ns with an only slightly lower output energy of 2.22\,mJ. Furthermore, using a simplified rate equation model, we discuss design constraints on the pump fluence in a pulse pump approach for Tm:YAG to maximize the energy storage capability at given pump power.