My Carrier (M#48GS-003060) heat pump compressor all of a sudden starting making a loud humming noise tonight, when I went to investigate I found the outside unit discharging hot air. Why would it be making the loud humming noise? Is the discharge of hot air related to the noise?

Did it go back to normal in a few minutes and was the fan off? If so, I think you just watched a defrost cycle.

No the unit did not shut off - it stayed on. It is 60 degrees outside so I would not think it would need to go through a defrost cycle.

You don't have a heat pump based on the model numbers you posted, this model is a gas electric 2 1/2 ton with 60,000 btu's of heating. The noise may be the compressor or fan motor , it is best to try and determine which is making the noise if possible, it may be the contactor is stuck closed and not allowing it to shut down. Good luck, Mike