Let us assume that the temperature of the room is 25°C. The temperature will rise at first almost linearly, then the increase will gradually slow down, with a slow approach to 25°C. From 4°C to - say - 10-15°C, the increase is almost linear.
The curve should be almost exponential. But do not worry for this term: in this case, exponential does not mean that the temperature will increase faster and faster.
It is difficult to give an evaluation of the temperature reached after 4 hours. I think that, for 4 hours, it will be still increasing almost linearly. You could make an experiment: turn off for 30 min, an check how fast the temperature increases. Then multiply the increase by 8. E.g., if you go from 6 to 7°C in 30 minutes,, then in 4 hours you will reach approximately 14°C (something less).
The idea of storing water is good. Try to avoid thermal insulation around them.
Another idea, maybe trivial: try to decrease as much as possible the temperature of the room. If it decreases to 15°C, the temperature increase in 4 hours will be one half.