This paper presents the findings of a case study with building simulation using EnergyPlus dynamic thermal simulation software, in which wall insulation was varied together with cooling set-point temperature in a hot and dry climate of Botswana. Against the established norm that adding wall insulation reduces annual fuel consumption, it is shown in this paper that this is not always the case: there are instances where adding wall insulation directly increases annual fuel consumption. Initial cost of insulation aside, as the cooling set-point temperature is gradually increased, the building switches from an "insulation reduces cooling load" to an "insulation increases cooling load" behaviour. In other words, the well established knowledge that "the lower the u-value the better" gets overridden by "the higher the u-value the better". We termed this a "point of thermal inflexion". Simple graphical demonstration of the existence of this point is presented in the paper. According to the findings, design engineers and building economics related professionals who quantify investment on insulation can get disastrous results if they assume that all buildings behave pro-insulation since a building may behave anti-insulation. (C) 2008 Elsevier B.V. All rights reserved.