Christmas Tree Water

What's the best way to serve water to your Christmas tree? I know that the first batch should be hot (to get that caramel-like sap moving), but should each new addition be hot, too? (Although that just means the tree gets warm water, since the stuff already in the holder is cold.)

Also, in vases of flowers, I always add a teaspoon bleach to keep the water from getting algae-y and smelly. Do some add bleach to their tree water? Or soap, maybe?

Does it make a difference to your answer if you knew that the cat needs to "hunt" for his water, and so prefers toilets, tubs, and Christmas trees as his hunting grounds?