Mrs B was musing about the thermodynamic implications of this cafe sign. We only talk about heat moving, not cold. And we stress that it is "heat energy" - and modern syllabuses change that to "thermal energy" because we need to stress the difference between heat energy and temperature. Thermal energy is essentially atom wobble. Things with a high temperature have furiously wobbling atoms. We say they are hot. The universe is quite egalitarian and tries to equalise out the amount of atom wobble so ones with more can give to ones with less, but not vice versa. The actual situation is even more complicated because we normally deal with whole objects - collections of millions of atoms. Even an object that feels cold can have a few atoms that wobble massively. So a cold object could pass energy to a hot object but the net flow would be from hot to cold. So physicists tend not to draw arrows labelled "cold"!
