Baby, it’s cold outside — but not in this penthouse co-op. (Though its price is high enough to freeze out most New Yorkers.)

Jo Sullivan Loesser — the widow of composer Frank Loesser, who penned that Academy Award-winning song and also wrote the music and lyrics for “Guys and Dolls” — is selling her Midtown duplex for $4.5 million.

The four-bedroom, three-bathroom abode at 410 E. 57th St., between First Avenue and Sutton Place, is 3,053 square feet.

It comes with 2,150 square feet in wraparound terrace space and views of the East River and the Queensboro Bridge.

The penthouse’s music room features the piano where Loesser composed many of his famous songs and a marble woodburning fireplace.

There’s also an “informal” living room with another fireplace that opens to a dining area and an aquarium that separates it from the chef’s kitchen.

The duplex also features a glassed-in wall with a staircase that leads to a suite with a third wood burning fireplace, a library and a kitchenette.

Building amenities include a gym and landscaped garden.

Corcoran’s Dee Downing has the listing.