In order to apply a Godunov method to steady and unsteady thermical flows, we first present a truncation error analysis which proves that the Turkel preconditioned Roe splitting is applicable to flows modelized by the classical low Mach number model, including thermics. The impact of the Turkel preconditioning on the first-order/second-order pseudo-Newton algorithm (referred in the literature as the defect-correction iteration) is also analysed. Implicit methods for steady flow resolution and for accurate unsteady time advancing are proposed and studied. Numerical illustrations involve the natural convection in a square box and a flow around a perforated wall inspired by helicopter engine applications. (C) 2003 Elsevier Ltd. All rights reserved.