To assure adequate fire performance of concrete structures, appropriate knowledge and adequate, practical models of concrete at elevated temperatures are crucial yet current lacking, prompting further research. This paper first highlights the limitations of inconsistent thermal boundary conditions in conventional fire testing; and of using constitutive models developed based on empirical data developed testing concrete under minimised temperature gradients in modelling of concrete with significant temperature gradients. On that basis, the paper outlines key features of a test setup used for the accurate control of the thermal boundary conditions when testing concrete at elevated temperatures, using radiant panels to generate well-defined and reproducible heating regimes. The repeatability, consistency and uniformity of thermal boundary conditions are demonstrated using measurements of heat flux and in-depth temperature of test specimens. Compressive strength is also investigated. The initial data collected clearly suggested that the incident heat fluxes, and thus the associated temperature gradient, has potentially significant effects on concrete mechanical properties at elevated temperatures. Further research is thus ongoing to quantify such effects and also to develop constitutive models accounting for a wide range of heating conditions; from very slow to extremely rapid heating. The proposed models could be included into effective rational knowledge-based fire design and analysis of concrete structures.