Grumbling noise when engine cold
 

Just got my new (to me) 2003 Volvo S40. Love it to death, but there is one nagging issue. When you start it in the morning, or when the engine is cold, theres a strange grumbling noise; but only in reverse or drive. It sounds like its forward of the driver's seat, but that could just be because of where I sit in the car. After about 5 minutes of idling the noise is gone regardless of gear. Any ideas?

Loose baffle in your cat',or exhaust muffler.
Could be a loose/vibrating heat shield also?
Get under car when engine started cold and see if you can home in on sounds origin.

If there was something loose, why would it stop when the engine warmed up?

Does it coincide with stepping on the brake pedal? Could be the electric brake motor. I have no idea what it does but I hear it when the car is first started and backed out of the garage. I'm thinking it may pull vacuum for the brakes while the engine vacuum is low.

It actually only happens when you release the brake and let the car start moving. And only when it's in gear. And even then after the engine is warm it's gone.

Loose baffles and exhaust parts often quieten down once the exhaust gets hot and the metal baffling inside expands enough to stop rattling loosely inside.
If it is that you will hear it if your underneath when its running cold at startup.
When you slip her into gear it can get louder too.
Maybe check your exhaust support brackets beneath the car also.
Are your engine / transmission mounts all ok?

The sound Hudini has described is what I get when reversing from garage also.
Mine however, (V40 2002) is not a grumble, just a very subtle whine as is typical of hydraulic systems.