In this paper we consider a nonlinear heat equation describing thawing and freezing of permafrost soils with the time varying surface boundary condition. We compare two schemes for time discretization: a conservative fully implicit one and a non-conservative sequential approach which uses the so called apparent heat capacity. We show that the differences between the schemes can be significant if the time step is large and when the inputs to the problem change abruptly. We also show that a simple variant of sequential scheme with arithmetic average and an extra iteration does not give consistency but gives better agreement with the implicit approach.