I use slightly warm water to keep the root-zone warm, indeed.
It makes sense to me, although I don't have any empirical evidence.
Here's my logic, however:

Warm water penetrates and saturates soil media more effectively.
It also dissolves salts more readily, which helps to flush old solubles
from the mix, as well as deliver a fresh dose of nutrients when fertigating.
Also, warm water is closer to vapor form than cold water - so it seems that
warm water will become available to roots and will "dry" sooner.
During the winter, I try to water my succulents with warm water in the morning.
This gives the media a full day to dry before night-set.

Recently, I've re-potted several chile plants. After potting, I watered
my plants into their containers with warm water. I've heard that peppers
slip into a dormancy when their root-zones are consistently below 50 degrees,
so I wanted to keep them in an active growth state when transition from garden
to containers indoors.


Josh