This contribution describes a set of equations and relations to calculate accurate cooling paths through the 2D temperature field of an exhuming region with periodic topography. A 1D model adequately captures the time-varying component of the system, making the computation efficient. A series of 2D finite element models demonstrate how temperatures below the periodic mid-slope, or mean topography, can be mapped to those below ridges and valleys, and how these transitions vary with topographic period and amplitude and the ratio of the near-surface geotherm to the atmospheric lapse rate. These new calculations are implemented into HeFTy to support multi-sample modelling of samples collected along topographic profiles, particularly for terranes with long-lived topography that exhumed through an inflected temperature field.