Non-asymptotic numerical simulation of transient heat transfer requires knowledge of initial conditions. If the heat transfer medium is ground, they typically use temperature logs (depth-temperature tables) of monitoring wells for the initial time point. Then one may either use scattered-data interpolation  or solve a steady heat transfer problem with Dirichlet boundary conditions at temperature measurement points. If you choose the second way and the problem is nonlinear, there might be some convergence issues.
Figure 1: Ground Temperature Interpolation in Frost 3D Universal