Designing a growing box using a resistance wire as a heating element
First of all, I need to determine how much power is required to heat up the box to the target temperature. Let's assume that the temperature is 20°C and I want to heat it up to 30°C in 30 minutes.

Not the way most of us would go about it. Your long term load is the heat loss through the walls. You have to make sure you have enough power to support that. Once that's done, the actual heating time doesn't really need to be specified, it will take whatever time it takes to get up to temperature. With the timescales associated with a grow box, 30 minutes seems unreasonably fast. We can see how near to that we'll get later when we have estimates for power, and the mass of what's in the box.
Estimate the heat loss of a box with volume 1 m3. Make some assumptions, it's easy to modify the answer later if any are grossly wrong. This will produce an absolute minimum answer, you'll probably want to use 2 to 10 times this figure, for safety.
Surface area of a regular 1 m3 cube A = 6 m2
Thermal conductivity for new PU insulation foam K = 22 mW/K/m
Foam thickness t = 50 mm
Temperature rise of box dT = 10 °C
Heat loss = dT.K.A/t = 26 W
That's the best case. As the foam ages, K will increase. Any wires passing through, or air leaking in or out will increase the loss. Using a cuboid rather than a cube will increase the surface area per volume. Any thin spots, or structure passing through the foam, aka 'cold bridging', will increase the loss. If your ambient drops and you need more than 10 °C rise, or if you use a lesser insulation material like polystyrene or rockwool, or a thinner wall for cost reasons, your power requirement will increase.
You might get away with 50 watts if you use new PU of at least that thickness, well air-sealed, but 100 watts would give you more margin for construction defects.
At this power level, incandescent bulbs, for instance auto bulbs or MR16 spot lights, make an excellent low cost self-indicating heater. Needless to say, you will not be using batteries. For those 12 V heaters, an old ATX PC power supply would be good, having as it does a 5 V output for the electronics as well.
Don't forget you need to raise the temperature of the soil, its moisture content, and the inside of the walls of the box, as well as the air. The temperature may take a long time to become uniform throughout the soil, 30 minutes would be nowhere near enough.
The thermal capacity of soil varies enormously depending on whether it's mostly dry vermiculite, or very wet loam. If we make the assumption of 50 mm soil thickness and 30 % moisture, that's 15 kg of water, even neglecting the soil itself. The thermal capacity of 15 kg water through 10 °C is 15x4200x10 = 630 kJ, which is about 2 hours at 100 watts. This suggests a warmup in less than 24 hours is quite possible, and a 30 minute one would need unreasonably high power.
If this is a grow box, then presumably you will need a light source in there as well? Perhaps switching your light source between LEDs and MR16s would modulate the heat input into the box enough to give you control?