The Fourier heat conduction equation is derived and stated in various coordinate systems. Six sets of boundary conditions, along with the appropriate initial condition, are introduced: (1) prescribed surface temperature; (2) the adiabatic surface; (3) prescribed heat flux; (4) heat transfer by convection; (5) heat transfer by radiation; (6) heat transfer by convection and radiation. Detailed solution methodologies for one-dimensional temperature variations are provided by the separation of variables method and the Laplace transform technique in Cartesian, cylindrical, and spherical coordinate systems. The temperature distributions in a strip, a solid cylinder, a hollow cylinder, a solid sphere and a hollow sphere are described in detail.