Expansion of an HII region in a homogenous medium (n_H = 500 cm^-3, T ≈ 25 K, S_∗ = 10⁵⁰γ_ionizing/s). Case 1 is a simulation where the gas temperature is instantaneously at 7736 K if the ionization fraction is exceeds 0.5. Case 2 takes into account the time evolution of the temperature given by Eqs. (9) and (10). The analytic solution is computed from Eq. (12) if the thermal equilibrium is reached instantaneously. The Strömgren radius is given by Eq. (11).