T HE heat transfer across irregular surfaces, such as perforated plates, has been extensively studied in the past to control the rate of thermal energy in heat exchanger devices. In some cases the use of perforated plates within ranges of temperature at which the material that constitutes the plate exhibits a temperature-dependent thermal conductivity is unavoidable. This makes necessary the study of the influence of variable thermal conductivity of perforated plates on heat conduction processes in order to improve the design and construction of the involved equipments. Over the past years, important research efforts have been devoted to the study of surfaceswith circular and elliptical perforations for the design of plate fin and tube heat exchangers, like those of RomeroMendez et al. [1], Mon andGross [2], Erek et al. [3], andWu and Tao [4]. Experimental research has been developed in the works of Kim and Song [5] and Saboya and Saboya [6]. Also, remarkable numerical studies have been done for the problem of heat conduction over surfaces with complex geometries like the one of Blyth and Pozrikidis [7], in which the heat conduction over irregular and fractal-like surfaces is analyzed. In the analysis of combustible flow around catalytic wires of circular section, the geometry of the system is similar to the one studied in the present work, making possible the use of the methods applied to such problems, like those found in the work of Vera and Linan [8], and that of Lizardi et al. [9], who studied combustion problems around catalytic wires. In the study of the effects of variable thermal conductivity in heat transfer processes, a great advance in research is achieved. Representativeworks are those ofHung andAppl [10],Aziz andHug [11], Krane [12], Muzzio [13], Aziz and Benzies [14], and Aziz and Na [15], who have extensively applied regular perturbation techniques to clarify the role of variable thermal conductivity on the performance of longitudinal fins. Chiu and Chen [16] used a decomposition method to evaluate the efficiency and the optimal length of a convective fin with variable thermal conductivity. Later, Lizardi et al. [17] studied the conjugate film condensation heat transfer process in a vertical fin with temperature-dependent thermal conductivity using perturbation techniques and numerical calculations. In this Note, the effect of a circular perforation combined with that of a variable thermal conductivity in a heat-conducting rectangular plate is studied.