In this article, we utilize the finite Sine-Fourier transform (FSFT) and the Laplace transform (LT) for solving fractional partial differential equations with regularized Hilfer-Prabhakar derivative. These transforms are used to get analytical solutions for the time fractional heat conduction equation (TFHCE) with the regularized Hilfer-Prabhakar derivative and with heat absorption in spherical coordinates. Two cases of Dirichlet boundary conditions are considered with obtaining analytical solution in each case. The effect of the parameters of the regularized Hilfer-Prabhakar derivative on the heat transfer inside the sphere is discussed using some figures.