In this paper steady heat conduction in Cartesian coordinates is discussed with the method of Green's functions for the slab, the rectangle, and the parallelepiped. The commonality among the components of the GF for 1-D, 2-D, and 3-D bodies is emphasized. The relationship between higher-dimension Green's functions and the lower-dimension Green's functions is discussed. There are at least two and sometimes several alternative expressions for each Green's function, and the alternative Green's functions are very important for construction of rapidly-converging series useful for numerical evaluation. A Green's Functions Library is described in which the Green's functions are organized according to a unique numbering system and are available on the world-wide web (http://www.engr.unl.edu/~glibrary/).