Fermentation Temps?

I keep my house at 70* 24/7. But my primary says its closer to 78*. I understand that the activity of the yeast generates a small amount of heat, and the plastic bucket acts as an insulator. I would like to bring my temps down to around 70*.
My question is this:

Can I immerse my bucket in room temperature water? If the water stays at room temp, maybe that would help keep my ferment temps down?

Yes, you could do that. You could also put a bottle of ice in that water bath, too. I do that and keep a floating thermometer in the water. The water would be the same temperature as the beer. Another benefit for the water bath is it keeps temperature fluctuations to a minimum- it takes a long time for that much water to change temperature.

You could also do the towel and fan "trick"- put the towel in the water so it wicks up the side and blow a fan on it. This really has great cooling. I have an igloo cooler that I made a styrofoam lid for that works great. I just put some water in it and change out frozen water bottles every day or so. (See my gallery for pics).