An analysis is made of the thermal processes associated with the presence of a local heat sink (or source) on the convectively cooled surface of a solid. The sink is due to the presence of a surface-mounted thermocouple, a pin fin or other surface-mounted conductors. In the first part of the paper, heat transfer results and temperature distributions for the solid are determined in general, without reference to specific applications. The results are then applied to the case of the surface-mounted thermocouple, and the error in the measured temperature owing to the presence of the thermocouple is evaluated. Application is also made to pin fins and other surface-mounted conductors, and heat transfer rates are calculated taking into account the depression of the base temperature owing to the interaction of the fin (or conductor) and the solid. It is found that the conventional calculation which neglects the base temperature depression overestimates the heat transfer rates.