The intrinsic thermocouple problem has received considerable attention over the last two or three decades. The most common geometry for the intrinsic thermocouple problem is a semi-infinite cylinder (wire) attached perpendicularly to a semi-infinite solid (substrate). In this paper the transient thermal behaviour of the interface between the thermocouple wire and the substrate due to step change in the substrate temperature is investigated using the multinode unsteady surface element (MUSE) method. The method uses Duhamel’s integral and involves the inversion of a set of Volterra integral equations, one for each surface element. The solution is obtained for a wide range of dimensionless times. The results show excellent agreement between the present solution and the other existing solutions. Very high accuracy is attainable with a relatively small number of surface elements for the complete time domain. This feature makes the method superior to alternative numerical techniques such as finite difference or finite element that involve whole-body discretization.