A catheter includes a cryoablation tip with an ablation assembly for heating tissue. The cryoablation tip may be implemented with a cooling chamber and have an RF electrode at its distal end. The electrode may be operated to warm cryogenically-cooled tissue, or the coolant may be controlled in combination with an RF treatment regimen to enhance the lesion size, speed or placement of multi-lesion or single lesion cycles. In one embodiment a microwave energy source operates to extend beyond the thermal conduction depth, or penetrate the ice ball and be absorbed in tissue beyond an ice boundary, thus extending a dimension of treatment. Also, the cooling and application of RF energy can be controlled to position the ablation region away from the surface contacted by the electrode thereby leaving surface tissue unharmed while ablating at depth or to provide an ablation band of greater uniformity with increasing depth.