I put the tubes containing pollen I will use in a microfuge rack like this:
Mine is dark green because that is what I found on the 'free' shelf in the department one day.
I take that and my note pad with the crosses I intend to make, out into the yard and go to work. It takes very little time for the pollen to 'thaw' and in reality I don't think it needs to be a certain temp before you use it, but it will need to thaw before it is activated. I've not had any trouble doing it this way. I am careful to keep the rack in the shade.
When I'm done I close the tubes and put them back in the freezer.