Cold weather driving

[BigDiesel3]

Hey guys I just bought a 2002 f350 7.3 dulley. It's been very cold where I live (single digits at night low teens during the day). I plugged in my truck over night and started it about 15 min before I leave. It makes a noise that clearly sounds like its not warmed up enough after 15 min. SO my question is.... If I don't let it warm up enough and I hear that same noise when I drive down the road will it hurt anything????