We present in this short communication the true form of Joule heating in CE which considers the contribution of surface conductance. This increased conductivity of electrolyte solution within electrical double layer has never been discussed in previous studies. The resultant intensive heat generation near the capillary wall is demonstrated using numerical simulation to produce not a locally strong temperature rise, but an additional temperature elevation in the whole solution compared to the model neglecting surface conductance. The latter effect is, however, negligible in typicall CE while it might become significant in very small channels.