In the solar corona, magnetically sheared structures are unstable to both tearing and thermal instabilities in a coupled fashion. However, how the choice of linear perturbation modes influences the time-scale to achieve the thermal runaway in a coupled tearing-thermal coronal current sheet is not well understood to date. Here, we model a force-free Harris current sheet under solar coronal conditions to investigate this coupling in the linear and non-linear regimes. In the linear regime, we adopt the magnetohydrodynamic spectroscopy code LEGOLAS to compare the current sheet under thermal and thermoresistive conditions, after which we initialize non-linear simulations (with MPI-AMRVAC) with the unstable, linear tearing and thermal perturbations obtained with LEGOLAS. It is shown that part of the unstable thermal quasi-continuum adopts tearing properties in the linear stage, but that it is not until the non-linear stage is reached that a true thermal 'runaway' effect leads to condensations inside tearing-induced flux ropes. Hence, the linear stage is governed by the dominant tearing instability whilst condensations form due to tearing-thermal coupling in the non-linear stage. Our results imply that perturbing an equilibrium current sheet with the fastest growing linear mode skips the mode-mixing phase in which the dominant instability traditionally emerges, and significantly reduces the time-scale to enter into the non-linear stage and thermal runaway process from its equilibrium configuration.