This is a rather esoteric question and I don’t think you will find the answer in books on the domestic cat but you will find opinions on the Internet. I think you have to work out an answer based upon common sense and upon the origins of the domestic cat.
I’ve said it before many times, the North African wild cat is the wild forerunner of the domestic cat. This wild cat species drinks water from streams. The water is often cooler relative to the ambient air temperature and the temperature of the land upon which the cat walks and runs. In short, the water is often cooler than any other aspect of the wild cat’s environment. This certainly won’t always be the case. Stream water is often cooler because it might be groundwater. There may also be the cooling effect of the latent heat of evaporation. However, a still puddle would not be cooler.
Therefore I would suggest, humbly, that it is likely that domestic cats prefer cool water, in general. I say “in general” because this answer cannot apply across the board. It comes down to individual cat preferences at the end of the day.
That said, I don’t think it makes an awfully big difference whether the water is cool or neutral in temperature. If your cat is a poor drinker you might like to try cooling it to see whether that encourages drinking. An alternative trick is to change the bowl. Some people think that a clear water bowl is preferable, for instance.
Another factor influencing whether a cat likes or dislikes their water is the chemicals in it. Tap water contains chemicals such as fluoride or chlorine to make it more hygienic for people. Domestic cats can taste this. This is why they prefer puddles of water outside the home which to the human eye look very unhygienic but the water tastes better to a domestic cat.
This assessment suggests that people should provide bottled water or filtered water if they wish to encourage the cat to drink. Milk, as we all know by now, is not an ideal drink despite tasting good to a cat due to its fat content. This is because in general, domestic cats are lactose intolerant and, therefore, if given too much milk it can cause digestive problems and perhaps diarrhoea.
All domestic cats are relatively poor drinkers because that is the way they’re built and this aspect of their character is a weakness if their main food diet is dry. The domestic cat will obtain most of their water from prey and therefore if you want to replicate that with commercial cat food it should be wet cat food which contains a similar amount of water to an ideal prey item for the domestic cat such as the mouse (around 70% for a mouse and 80% for wet cat food).
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