The invention concerns a catheter for intravascular application, comprising a shaft extending along the catheter longitudinal axis from the proximal end to the distal end and having a fluid-tight shaft wall and at least one lumen which is adapted to guide a fluid and at least one electrically conductive wire which extends from the proximal end at least into the proximity of the distal end of the catheter along the catheter longitudinal axis. The catheter is characterized in that on at least one portion length of the catheter which is provided for introduction into a body, a lower level of heat-transmission resistance obtains between a fluid in the lumen and the electrically conductive wire than between the wire and the shaft wall so that heat produced in the wire can be effectively dissipated to a fluid flowing in the lumen, wherein the catheter includes at least one temperature sensor which is arranged to detect a temperature which in the case of heating of the wire depends at least predominantly on the heating of the wire.