This paper analyzes temperature measurements acquired in the offshore operation of a wave energy converter array. The three directly driven wave energy converters have linear generators and are connected to a marine substation placed on the seabed. The highly irregular individual linear generator voltages are rectified and added on a common dc-link and inverted to 50 Hz to facilitate future grid-connection. The electrical power is transmitted to shore and converted to heat in a measuring station. The first results of temperature measurements on substation components and on the stator of one of the linear generators are presented based on operation in linear and in nonlinear damping. The results indicate that there might be some convective heat transfer in the substation vessel. If high power levels are extracted from the waves, this has to be considered when placing components in the substation vessel in order to avoid heating from neighboring components. The results also indicate that the temperature increase in the linear generator stator is very small. Failure due to excessive heating of the stator winding polyvinyl chloride cable insulation is unlikely to occur even in very energetic sea states. Should this conclusion be incorrect, the thermal conductivity between the stator and the hull of the wave energy converter could be enhanced. Another suggested alteration is to lower the resistive losses by reducing the linear generator current density.