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We study the effective heat conductivity k of a periodic cubic array (with side length l) of perfectly conducting spheres of the volume , 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 → 0 and asymptotic formula for → π/6 (limiting value of sphere) and as a tool--quasifractional approximants.