An electrosurgical medical device and method for creating thermal welds in engaged tissue. In one embodiment, at least one jaw of the instrument defines a tissue engagement plane carrying a conductive-resistive matrix of a conductively-doped nonconductive elastomer. The engagement surface portions thus can be described as a positive temperature coefficient material that has a unique selected decreased electrical conductance at each selected increased temperature thereof over a targeted treatment range. The conductive-resistive matrix can be engineered to bracket a targeted thermal treatment range, for example about 60°C, to 80°C., at which tissue welding can be accomplished. In one mode of operation, the engagement plane will automatically modulate and spatially localize ohmic heating within the engaged tissue from Rf energy application-across micron-scale portions of the engagement surface. In another mode of operation, a conductive-resistive matrix can induce a "wave" of Rf energy density to sweep across the tissue to thereby weld tissue.
