An analytical solution has been found for the simplified time-dependent transport equation in a finite cylinder. This solution represents a decomposition of the heat source in eigenmodes. Their eigenvalues represent the effectiveness of the response to temperature for each eigenmode, which are different in the stationary regime: the higher the order, the lower the effectiveness. In this case, the response to temperature appears as non-local. On the other hand, the profile resilience mainly results from two effects: the first one is that the lower order eigenmodes are more favoured than the higher order; the second one (volume effect) is that the central source (Ohmic heating) is favoured with respect to the off-axis source (electron cyclotron resonance heating, ECRH) in the contribution to the temperature profile shape. This resilience effect on the temperature profile is a basic and natural property of the diffusion equation in cylindrical geometry. The above analytical solution has been used for the determination of the heat diffusivity χ and the damping time τd for the ECRH modulation experiments in the Tore Supra tokamak. The results obtained by this analytical method have been compared to those obtained by two other methods: the FFT and the power balance methods. The FFT is the easiest and the fastest method compared to the others, but it is too sensitive to perturbations such as the sawteeth, which may cause inaccurate results. The analytical solution is the most robust method, because it simulates the whole temperature modulation; hence, the results are less sensitive to other perturbations. Furthermore it contains more information than the FFT method. For 0.2 ⩽ r/a ⩽ 0.7, the values of χANA are very close to those of χPB during the ECRH phase. Generally, the values of χHP, which is more 'transient', are larger than those of χANA and χPB (ECRH).