Steady-state heat conduction is considered for perforated thin plates with non-insulated facial surfaces. The heat conductivities of the materials and the convection coefficients are assumed piecewise constant. Influence functions of point sources are analytically obtained for some such plates of standard shape. Their singular components are derived in a closed form, ensuring accurate straightforward computer implementations. Special integral representations are then used for obtaining influence functions of a point source for perforated plates. Computability of those representations is tested with a number of illustrative examples.