delta temp = 0.46 degrees C in one second
temp @ 1 min = 27.78 degrees C in a 1minute
Let's try to work out the steady-state temperature if it were sealed.
Work out the thermal conductance of the walls of the box. The area is about 2 m^2. If it were 10 mm plywood, the conductance would be about 0.13 W/mK * 2 m^2 / 0.01 m = 26 W/K
So your 100 W input would cause the internal temperature to reach about 4 C above ambient, with a sealed box.
But you want a temperature rise of 60 C, i.e. 15 times that.
Insulating materials like felt and polystyrene are probably about 5 times more insulating than that plywood. So maybe 30mm of polystyrene would be enough to give a steady-state sealed box temperature of 60 C.
Of course you want a fan to remove the moisture. If you want to really over-engineer the thing, make a heat exchanger so that the extracted moist air warms up the incoming dry air!