Summary: A stationary heat conduction problem is investigated in composite materials with two small parameters \(h\) and \(\varepsilon\). A method is proposed and justified for constructing an approximate solution of any order. A fundamental feature of the method is that the approximate solution is sought in the form of a power series in \(\varepsilon\) and \(h/\varepsilon\) corresponding to the essential nature of this type of problem. An averaged equation is obtained to any order of accuracy, and an asymptotic solution of the original equation is constructed that avoids operations with small parameters. Moreover, the scheme proposed does not require the numerical solution of 3-dimensional elliptic problems inside each periodic cell.