The paper presents the efficient parallel algorithms for solving the heat equations for the permafrost models. By using the finite difference scheme, we transform the Stefan problem into the problem of solving multiple systems of linear algebraic equations. These systems have tridiagonal coefficient matrices and are solved by the sweep method. On the base of the parallel algorithms, we developed the codes for multicore CPU with OpenMP technology and for GPU with CUDA technology. The novel approach was proposed to achieve the efficient memory access patterns. Numerical experiments show that our new code is up to 2x faster than the previous one, and the GPU implementation achieves a tenfold speedup compared to the serial CPU code.