I think there are a few more things to consider. Based on that first law, the room would get hotter because you have the added heat from the pump.
I think you also need to take heat capacity into account.
http://en.wikipedia.org/wiki/Specific_heat_capacity
If you look at the table water has one of the highest abilities to store heat. When you use a heatsink, you pretty much immediately heat the air and move it to the air outside the case. This will raise the temp of the room quickly. When you use water, you have to use a lot more energy to raise the temp. This energy will not immediately leave the water and join the air. This means that it will take longer to heat the room with water, but if the ambient temp stays constant they should both achieve the same temp.