A lead for an implantable cardiac prosthesis, with protection against the thermal effects of MRI fields by terminating the lead head (10) with an electrically insulating tubular outer housing (28) and an anchoring mechanism. The tubular housing (28) carries an electrically isolated thermally conductive solid part in the outer region of its distal end forming a heat sink. The heat sink thermally conductive material is for example titanium, associated with an electrically insulating coating such as a diamond deposition. The anchor may be a projecting helical anchoring screw (20), axially extending the tubular housing, which is an electrically conductive active screw on at least one end portion.