The step response of a single-pass crossflow heat exchanger with variable inlet temperatures and mass flow rates was determined. In every instance, the energy balance equations were solved using an implicit central finite difference method. Numerical predictions were obtained for cases where both the minimum or maximum capacity rate fluids were subjected to step changes in inlet temperature, coupled with step mass flow rate changes of the fluids. Likewise, performance calculations were conducted for heat exchangers operating initially at steady state, where step flow rate changes of the minimum and maximum capacity rate fluids were imposed in the absence of any temperature perturbations. Because of the storage of energy in the heat exchanger wall, and finite propagation times associated with the inlet perturbations, the outlet temperatures of both fluids do not respond instantaneously. A parametric study was conducted by varying the dimensionless parameters governing the transient response of the heat exchanger over a representative range of values.