Air cooling of high-temperature gas turbines is a standard practice; the air first cools the blading by internal convection and then by external film cooling, after ejection through holes and slots in the blade surface. In some ‘conventional’ analyses of turbine blade cooling, a ‘standard blade’ is invoked, which has a uniform blade temperature equal to the average temperature of the real blade, and estimates are made of the cooling flow required to hold the standard blade temperature to a limit set by material considerations. However, early analytical work by Ainley (for convective cooling of thin-walled blades) showed that both the coolant and blade temperatures should increase along the blade span. The current paper develops Ainley's original analysis to allow for finite blade wall thickness and thermal barrier coatings, film cooling, and variation in the mainstream gas temperature along the span. This new analysis should enable more accurate estimates to be made of cooling air flow requirements.