intravenous (IV) in the tail vein of an anaesthetized mouse
Cleaning the tail with ethanol is of some help and also, as you said, warming the tail. We sometimes put one of those flexible lamps (such as this) to heat up only the tail.

When anesthesized (ketamine/xylazine or isoflurane) we keep our mice on a heated pad anyways.

Cannulation in the tail does not sound like a good idea to me, especially if you are going to have the animal wake up afterwards. If you're going to cannulate then go for the jugular, but be aware that doing it on a mouse requires quite a bit of experience and it's definitely way longer than a tail injection.

It really depends on your experiment