I don't think the temp makes that much difference. If you are worried about them being chlled, give it room temp. If they are hot, give it cold.
Ellie drinks from the tap because that's what I do. It is served cold because we don't drink the warm or hot from the tap ourselves but by the time she drinks it, it is probably room temp. I would have no problem giving her very cold water from the fridge but that's not what I use, so neither does she...
I try to change water twice daily but her bowl just gets rinsed. I don't wash it everyday. It gets changed every couple-few days. It would definitely be better to wash it daily, but it seems clean enough by just rinsing it.