Neoclassical Tearing Modes (NTMs) are widely observed in tokamak plasmas. They have a detrimental effect on plasma confinement and may even lead to disruptions. Therefore it is important to understand the evolution of NTMs, which is influenced by several effects. These effects are summarized in the Modified Rutherford Equation. The TCV tokamak is equipped with very flexible heating systems and extensive magnetic and kinetic diagnostics, and is therefore very suited to study NTM evolution. In many experimental sessions at TCV the general NTM characteristics were studied. An important question is the relative importance of the effects of heating and current drive of ECRH/ECCD on the evolution of the NTM; in many modelling efforts in the past the effect of heating was neglected. A series of dedicated TCV experiments was devoted to disentangle these roles in the suppression of the m/n = 2/1 NTM: the NTM was triggered by central co-ECCD using two gyrotrons, and then it was tried to stabilize this NTM with a third gyrotron whose deposition location was swept from the centre towards the q = 2 surface. In otherwise similar discharges, this third gyrotron was delivering either co-, counter-ECCD, or pure ECRH. In the experiment a clear difference in NTM stabilization was observed between these discharges. The main aim of the present work is to reproduce the different time evolutions as described in the previous paragrah, and decide from this whether the effect of heating is essential to capture the time evolution of the NTM. This is done by simultaneously modelling the evolution of the NTMs and of the current density and temperature profiles. For this purpose the Rapid Plasma Transport simulatOR (RAPTOR) is used [F. Felici et al, Plasma Phys. Control. Fusion 54 (2012) 025002]. It has a module that solves the NTM evolution based on the Modified Rutherford Equation. RAPTOR self-consistently calculates the simultaneous evolution of electron temperature, q profile and NTM width. It is shown that the triggering and suppression of the m/n = 2/1 NTM in TCV by varying the ECCD deposition and by varying the sign of the CD, can be described well by the Modified Rutherford Equation. Moreover, it is shown that the Heating term in this equation is essential to fully capture the observed dynamics.