Accurate convective heat transfer predictions are required in building engineering and environmental studies on urban heat islands, building energy performance, building-envelope durability or conservation and (natural) ventilation of buildings. When applying computational fluid dynamics (CFD) for these computationally-expensive studies at high-Reynolds numbers, wall functions are mostly used to model the boundary-layer region. In this study, an adjustment to the standard temperature wall function is proposed for forced convective heat transfer at surfaces of typical wall-mounted bluff bodies in turbulent boundary layers, such as the atmospheric boundary layer, at moderate to high Reynolds numbers. The methodology to determine this customised temperature wall function (CWF) from validated numerical data of CFD simulations using low-Reynolds number modelling (LRNM) is explained, where a logarithmic-law behaviour is found. The performance of this CWF is evaluated for several bluff-body configurations. Standard wall functions (SWFs) yield deviations of about 40% for the convective heat transfer coefficient, compared to LRNM. With the CWF however, these deviations are reduced to about 10% or lower. The CWF therefore combines increased (wall-function) accuracy for convective heat transfer predictions with the typical advantage of wall functions compared to LRNM, being a lower grid resolution in the near-wall region, which increases computational economy and facilitates grid generation. Furthermore, this CWF can be easily implemented in existing CFD codes, and is implemented in the commercial CFD code Fluent in this study.