Moir\'{e} excitons (MXs) are electron-hole pairs localised by the periodic (moir\'{e}) potential forming in two-dimensional heterostructures (HSs). MXs can be exploited, $e.g.$, for creating nanoscale-ordered quantum emitters and achieving or probing strongly correlated electronic phases at relatively high temperatures. Here, we studied the exciton properties of a WSe$_2$/MoSe$_2$ HS from $T$=6 K to room temperature using time-resolved and continuous-wave micro-photoluminescence, also under magnetic field. The exciton dynamics and emission lineshape evolution with temperature show clear signatures that MXs de-trap from the moir\'{e} potential and turn into free interlayer excitons (IXs) at $T\gtrsim$120 K. The MX-to-IX transition is also apparent from the exciton magnetic moment reversing its sign when the moir\'{e} potential is not capable to localise excitons at elevated temperatures. Concomitantly, the exciton formation and decay times reduce drastically. Thus, our findings establish the conditions for a truly confined nature of the exciton states in a moir\'{e} superlattice with increasing temperature.