Will blowing a fan on milk help keep it cooler?

Ok so yeah. This is a weird one.... Just say if the weather is a little hot (and there's no air conditioning), and I've got say a bottle of milk I want to keep as cool as I can - and no other suggestion for keeping milk cooler is available (please do NOT suggest those solutions) - could a desk fan of all things actually help keep the milk cooler than if I DIDN'T blow the desk fan directly on the milk bottle? Thanks.