In most cryogenic applications, heat in leak from the ambient is a significant factor for the degradation in the performance of heat exchangers. The effect of heat in leak to the cold fluid in a three-fluid heat exchanger, for a cryogenic application, involving thermal interaction between all the three fluids, has been investigated using both the analytical and finite element methods. Cooling of the hot fluid has been identified as the objective of the three fluid heat exchanger. Seven non-dimensional parameters, including one to account for ambient heat in leak to the cold fluid, have been identified and their effects on hot fluid behaviour - temperature profile, effectiveness and degradation factor - have been studied. The results presented give valuable inputs towards better understanding of the behaviour of the hot fluid in this class of heat exchangers. (C) 2012 Elsevier Ltd. All rights reserved.