Learn English – phrase origin: “sent packing”

Heat/heater is slang for "gun" (definition #14) and to pack has an informal meaning "to carry, deliver, or have available for action" (v. tr. definition #8). So "packing heat" means that you are carrying a gun (and are ready to use it).

According to the Oxford English Dictionary, here is the first citation for this phrase:

1932 W. R. BURNETT Silver Eagle i. 7 ‘He don't even pack a heater.’ ‘Don't what?’ ‘He don't carry a gun.’

And the first citation I see that uses heat instead of heater (from an old dictionary):

1942 L. V. BERREY & M. VAN DEN BARK Amer. Thes. Slang §496/6 Pack (a) heat,..to carry a gun.

The word operator has had several slang meanings over time, according to the Oxford English Dictionary. A brief list of the time and definition of operator is:

1598: A person who performs a surgical operation or operations; an operating surgeon or dentist.

1611: A person who deals in quack medicines, etc. Obs.

1704: A person who commits fraudulent operations; a thief, a pickpocket.

1828: A person who carries on (speculative) financial operations. Also: a person adept at speculative or shrewd operations; (formerly) a person who acts in a cunning or underhand manner.

1838: A person who or company which runs a business, enterprise, etc.

1944: A person with a talent for seduction; a smooth talker.

The phrase smooth operator starts to appear in the late 1890s. For example, in "The Strange Schemes of Randolph Mason", it says:

Here, a smooth operator is someone who is "smooth" at running a business or set of financial operations (the senses from the earlier 1800s). This is not the only application of smooth operator. In the 1980s, the OED notes the following usage:

1980 Photo-Love Summer Spectacular 7/1 You're quite a smooth operator, what with names and telephone numbers just like that!

The "operation" has changed over time. In the 1700 and 1800s, the "operation" was financial--it referred to either theft operations, speculating on stocks (operate as a verb meant "To deal or speculate in stocks or shares; to buy and sell commodities as a broker"), or business operations. Then, in the 1900s, the "operations" referred to the "business" of playing at courtship and seducing women.

Thus, now a smooth operator can refer to the "business" of financial operations or seduction operations, with smooth modifying operator in a primarily (and possibly solely) negative way.