DWV Condensation

Hi all,
I have an older house I just bought.
All plumbing is copper including DWV.
I have one stack in particular ( DWV ) which is 2" copper.
It goes from first floor,through second floor (picks up another waste line) and throught the attic to vent out the roof.
It of course runs through a chase, but in some areas it is open to a confined space (underneath the stairs from 1st to 2nd floor).
My question is:
should it be insulated to avoid condensation.
My initial suspicion would be a "no" to the question unless it was under a constant drainage situation, which would change copper temprature significantly if draining for extended periods of time. It is not, it serves only 2 sinks and a shower.
Am I right? or should I insulate it?

Thanks to all who answer.
cheers,
Tin

No you should not need to insulate it. The only time it could concievably have a condensation issue is if there was a constant flow of cold water going down it and this would most likely be cured by replacing a leaking toilet flapper. Of course, a toilet would not be on a 2" line...

The water from the sinks and shower is warmish. Even the first flush from a toilet is water which has aclimated to more or less room temp in the tank. SO, I would not expect condensation to be a problem.

Thanks for the replies.

So, 2 responses, both in agreement, good.
I probably wouldn't have thought twice about it except, when I demo'd the walls to re-do the bathroom, I found the 2" copper line covered with a fibrous burlap like covering approx 1/4" to 3/8" thick (disintegrating). It's an old house early 1950's in B.C. Canada.
Maybe I'll wrap it anyway.

thanks for responding.

You do have somewhat more extreme climates than we have here in S. Calif. so a little insulation can't hurt!

Insulation might soften the sound of water draining, but other than that, shouldn't be needed.