In boundary layers under the influence of centrifugal force, Goerter vortices can create high-gradient velocity and temperature zones near the surface, enhancing heat transfer. The energy level of a saturated pair of steady Goertler vortices is sustained by centrifugal forces and decays slowly in the absence of these forces. Unsteady Goertler flows may also trigger the transition of a boundary layer flow. Here we investigate the influence of curvature variations on the development of the unsteady Goertler instability and heat transfer rates. Two values of the Prandtl number were analysed, namely 0.72 and 7.07. The in-house High-Order Parallel (HOPe) numerical code was adopted for the numerical simulations. The discretisation in the spanwise direction is carried out by Fourier transforms. In the streamwise and wall-normal directions it is adopted high-order compact finite differences. The time integration is done by a fourth-order Runge-Kutta method. The results show that the heat transfer enhancement is more accentuated for Pr = 0.72 than for Pr = 7.07. In the non-linear Goertler vortex region, average heat transfer rates maybe be higher than expected laminar boundary layer correlations. In the absence of centrifugal forces, Gortler vortices dissipate slowly due to viscosity.