A Stirling engine (1) to which an annular burner (2) is attached and is sealed to the engine by a flexible annular sealing member (5). An annular coolant channel (4) in the form of an annular coolant channel member (24) with a U-shaped cross-section attached to a mounting bracket (3) cools the seal (5). The channel member (24) has an upwardly extending annular flange (29) to shield the interface between the burner (2) and mounting bracket (3). An annular lip (33) extends from a lower region of the coolant channel (24) and the top of the sealing member (5) is fitted around this lip. The sealing member (5) is fitted in place after the coolant channel member (24) has been mounted to the bracket (3).