Based on experience with siliceous aggregate/OPC paste concrete it is generally believed that the compressive strength of unsealed ‘concrete’ declines sharply above 300°C. This is too pessimistic a view. A reassessment of the subject is given in this Paper, which considers material and environmental factors/mechanisms influencing the strength of concrete during the heat cycle and after cooling, not all of which necessarily result in strength loss. Design of concrete for better performance at high temperatures should aim at minimizing contributions to strength loss, while exploiting the processes responsible for gain in strength. It appears that, in its hydraulic state of binding, a rheological criterion limits the structural usefulness of Portland cement concrete to temperatures of 600°C. Today, many commonly used concretes lose considerable strength at temperatures above about 300°C. There is, therefore, scope for improvement in design within the temperature range 300— 600°C. Raising the ‘working’ temperature of the material means that a significantly larger proportion of a structure exposed to high temperatures will remain serviceable and reparable, thus bringing about significant economic benefits.