The paper describes an empirical thermal model which provides an estimate of stator- and rotor-conductor temperatures in an inverter-driven cage induction machine under both transient and steady-state conditions (of heating and cooling), and under constant and variable flux control. The model is based on a widely used thermal-torque derating for inverter-driven induction machines, and features a single frequency-dependent thermal resistance and time constant for each winding. It is easily implemented in real time for online thermal protection and compensation for winding-resistance variation. The technique is demonstrated on two 7.5 kW inverter drives to give temperature estimates to within 10 deg C for both transient and steady-state operation. This accuracy is shown to be sufficient to maintain torque output to within 0.01 p.u. in both voltage-forced and current-forced inverter drives. The model can be generalised for a wide range of machine sizes, without the need for specific physical details, by assuming that induction machines are constructed of similar materials, and have similar insulation thermal limits.