We present a diode-pumped, electro-optically Q-switched Tm:YAG laser with a cryogenically cooled laser crystal at 120 K. Output pulses of up to 2.55 mJ and 650 ns duration 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 only a 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 a given pump power.