Carbon filter for sure is what you need, but I don't think you should run hot water to the tank. I believe hot water breaks down the carbon very fast and is also difficult to regulate.
On my water changer, I only use cold water and do smaller water changes daily. When I had it running in its glory, I had it doing two 10% water changes daily on a 72 gallon. Shifter the temp by maybe a degree or two, but nothing that would cause stress on fish. You could probably do something similar.
If you use a sump for filtration, you can integrate the water changer in a lot easier and not have to deal with water level issues in the tank.