I have the exact same setup but throw a small powerhead in there just to keep the water oxygenated and a heater to keep the temp matched. Although i guess if ur just adding small amounts of water at each time it shouldnt make a big difference.
I know of no published data that indicates you should do anything to the water. If anything gets in the water (e.g., dust) of course you'll see the tds rise - so folks suggest you cover it.
Remember that DI water is aggressive, so consider this in storing water. People have reported phosphates leaching from some types of containers used to store DI water.
I don't know of any reason to routinely heat the water unless you are going to use a lot of it at once - like for a water change.