Energy savings in buildings can be achieved to a large amount by optimizing the insulation capabilities of its external walls. Typically such walls are multilayer structures whose insulation properties have a crucial dependence on the type, thickness and ordering of the materials employed in their construction. In this work, the heat transfer matrix approach is used for a quantitative analysis of heat conduction in one-dimensional multilayer structures under steady periodic conditions. In this way, some of the results previously suggested by numerical data are accounted for in a rigorous way. In particular, a fundamental inequality concerning layer order and its effect on the modulus of the temperature decrement factor introduced by a wall is derived. This provides a design criterion for building effective insulation structures. Another factor that can significantly affect the insulating performance of a wall is the number of employed layers, once the total extension of the wall, the total material amounts, and therefore the total thermal resistance of the wall, have been fixed. It is shown that, under specific circumstances, an optimum number of layers can be identified. The influence of layer order and distribution on the time delay that a wall introduces between outer and inner temperatures is also addressed. The presented results are illustrated by means of numerical examples that show how to control to a large extent modulus and phase of the temperature decrement factor of a multilayer wall. (C) 2016 Elsevier Ltd. All rights reserved.