An extreme simplification of the case is to use the next analogy to find a solution:
Current source I1 pumps certain heating power into the box. Its current in amps is the heating power in watts. The thermal capacity of the box +what's inside is the capacitance of C1. The temperature of the box air as kelvins is the voltage of NODE1.
There's leakage between the ambience and the box interior. The thermal resistance Rt, where ohms can be directly seen as kelvins per watt, determines together with the capacitance the time constant of the temperature change. The thermal resistance and the ambient temperature (=VA) determine how high a certain heating power (=I1) can finally lift the box interior temperature (=voltage of NODE1)
You do not know the capacitance nor the resistance but you can measure them. Put a few watt known heating power and follow how high the temperature finally rises. It and the ambient temperature give how much is the resistance.
When you know the resistance you can calculate the capacitance by letting the system cool. The temperature decays towards the ambient temperature with time constant R1 * C1.
After you know the resistance and the capacitance you simply calculate how much power (=I1) you need to the wanted temperature rise in the wanted time and how much power you need to maintain the wanted temperature. A circuit simulator can be used to search the initial heating power if you hate calculations with exponential and time constant.
You still need a thermostat to be sure no overheating occurs and to take into the account automatically the variations of the ambient temperature.
BTW. The capacitance in farads directly presents the the thermal capacity= watts per (kelvins per second) or as well =joules per kelvin.