A razor having a handle and a blade cartridge containing one or more blades includes an electric circuit with a battery power source for controlled direction of current flow through the one or more blades in order to heat the blades. The electric circuit further includes opposing electrically conductive contact leads, the battery power source, and an electrically conductive contactor in contact with an ON/OFF switch all housed on the blade cartridge. A housing for the battery and switch extends transversely in spaced and separated relation to the blades and defines a bridge structure over an open gap between the housing and the blades for allowing a directed stream of water flow to pass below the housing, through the gap and between the plurality of electrically conductive blades for rinsing debris from surfaces of the blades.