The Lawson and ignition criteria are sensitive to the plasma density and temperature profiles and it is found that peaked profiles lead to a considerable easing of these criteria, as well as to a significant increase in the average fusion power density. Space and time-dependent reactor plasma calculations show that these profiles may indeed be sharply peaked at the centre owing to alpha heating and to rapid diffusion near the edge. The thermal equilibria are sensitive to the size of the device, to the conditions imposed at the plasma boundary and to the fuelling profile. A comparison between tokamak plasma equilibrium parameters predicted by often used global energy balance models and by space-dependent calculations indicates that the global-model results can differ sharply from the space-dependent calculations with regard to mean temperature, mean density, particle confinement time and fractional burn-up. In particular, the fractional burn-up predicted from global calculations can be too high and therefore strongly affect the anticipated tritium inventory and re-fuelling problems in tokamak reactors.