We present an efficient computational method to calculate the temperature rise during MRI of tissue surrounding the electrodes of an active implanted lead. Inputs to the model are transmission line parameters as derived from electrical tests on the lead and the calculated tangential electric-field along the length of the lead during MRI. The method was validated by comparing measured and calculated temperature rises at the electrodes of a neurostimulation lead in a phantom test. The distribution of temperature rise in the tissues surrounding the electrode array was calculated for a whole body SAR of 2 W/kg. The maximum temperature rise was 5.4oC, which is expected to be safe, but more work would be required to assess uncertainty in this determination.