The dynamics of most civil engineering structures is affected by the ambient temperature. This raises the issue of discriminating changes in modal parameters due to damage from those due to such effects. A statistical parametric damage detection algorithm based on a null space residual associated with output-only subspace identification and a 2 test built on that residual has been designed by some of the writers. The purpose of this paper is to propose two extensions of this detection method which account for the temperature effect. The first extension uses a thermal model for deriving a temperature-adjusted null space. The second extension exploits the thermal model together with a statistical nuisance rejection technique. Both methods are illustrated on a laboratory test case within a climatic chamber.