Temperature and power are only loosely related, and by the thermal resistance between the item and its surrounds.
P = (T1 - T2) / R
where:
- P is thermal power transferred between two items
- T1 and T2 are the temperatures of two items
- R is the thermal resistances (K/W) between the two items.
In your case, T2 is ambient (say 20C) and T1 is the bath, which you want to be 38C. If it's poorly insulated, expect maybe 0.5K/W thermal resistance, which means that you need at least 36W of heating to maintain the 18C temperature difference above ambient in the face of heat conducting away from the bath. If it's well-insulated (maybe 10K/W), you will need only 1.8W to maintain temperature, etc. So the power required depends entirely on how you build your bath.
Once you start agitating, your heat losses go way up due to evaporation from all the splashing about of warm water. Even though you can face about 150W of heat losses including evaporation, that still means a tiny temperature shift if you have enough water. 20L at 4.2J/(g.K) is 84kJ/K of thermal mass so with no heater and 150W of heat loss, that's a temperature drop of 0.5C in 5 minutes, which is totally acceptable for C41 processing. If I were you therefore, I would not bother with the heater (because 12W is totally futile in the face of evaporation losses) but just use plenty of water (20L) in an insulated tub to minimise conduction losses and provide lots of stability.
The heater pad feels "hot" (probably 50-60C) because when not attached to a large item like a tub of water, it has high thermal resistance to ambient. So its temperature goes way up until the thermal power balances out the electrical power.
