We study the effective heat conductivity k of a periodic cubic array (with side length l) of perfectly conducting spheres of the volume phi, embedded in a matrix material with conductivity 1. We construct a sequence of quasifractional approximants for the effective conductivity. As the bases for the construction we use the perturbation approach for phi --> 0 and asymptotic formula for phi --> pi/6 (limiting value of sphere) and as a tool-quasifractional approximants.