Obviously, cold isn't a "Thing".

Coldness is the absence of heat, and when you add a cold ice-cube to a drink there are no particles of "coldness" flowing into the rest of the drink cooling it down - the heat of the rest of the drink (in the form of molecular kinetic energy) is flowing into the ice-cube, leaving less left in the resulting drink.

I understand all of that :)

But my question is:

If you were to model coldness conduction as a thing that flowed (just as we model heat conduction as a thing that flows), would you get accurate macro-level models?

Can you accurately predict, say, the effects over time of placing an ice-cube on the centre of a thin aluminium tray, by modelling the cold as flowing out from the the ice-cube. (In the same way that you could predict the effect over time of placing a cube of heated metal in the same place)

If yes, are the equations and/or constants different, or is it just "add a minus sign"?