You'll see it, hear it and feel it. Idle will race initially, as the ECM is programmed to fast idle to help get the fluids moving, warm up the engine - then you'll see / feel / hear the RPMs start to slowly drop. Will not necessarily drop down to steady state idle on a warm engine, but will be significantly be lower than when it first started.
Good example was this morning - ambient air temps were in the teens. Started my car - fast idle to about 1500 RPMs, then the revs dropped to about 1000 RPMs after about 30-45 seconds. That point, I shifted it into gear and slowly accelerated, refraining from WOT until I see the temperature gauge start to move from the bottom position. By the time I get to the highway, I've traveled about 3 miles in about 6 minutes and the car is pretty close to being fully warmed up.
If I had just idled the car - it wouldn't have reached that temperature even with 15-20 minutes of idling.
As for "if the car is not fully warmed up, leading to muffler/exhaust problems" - I've never heard of that. If anything, the opposite would happen - at idle speeds, the car cannot push out condensation as quickly as it could, leading to moisture building up and sitting in the exhaust system.