These are in the first place junmai sakes (junmai-shu); and also honjozo and regular sake (yes, there is also quite drinkable regular sake (although I prefer junmai-shu), as long as you check the label and stay away from those to which sugar and flavorings have been added!). And as a general rule, sakes made with the kimoto and yamahai methods are particularly suitable for drinking warm (sometimes even the ginjo's).
So the term "hot sake" is not really very good and I propose we start using the more fitting Japanese term "kanzake." "Kan" 燗 itself already means "warmed sake" or "warming up sake;" "kan wo suru" means "to warm sake" and "kanzake" is the normal term for "warmed sake."
Another point is how to warm your sake. The best way by far is bain-marie: just put the tokkuri with the sake in a container with hot water (not boiling or on the fire) and use a kitchen thermometer to check the temperature of the sake inside.
Kanzake is also the time to use your tokkuri (earthenware or porcelain sake bottle) and choko (sake cups). These are very nice for kanzake, but not very suitable for cold sake (a ginjo or daiginjo should have more space to breath and develop its aroma, so here a glass like a wine glass is best; and I like to drink my junmai-shu when cold from earthenware or glass cups that are larger than the usual choko). Collecting such tokkuri and choko from different areas of Japan (which all have their own type of earthenware) is great fun, even more so when using them for your winter kanzake!