Years ago I kept some of my pins in a cottage on the property which we rarely use.It is fully finished.Without heat the temp would get down to 55F in the winter.I thought all was good until spring when I pulled them out.I totally planked out a diamond plated Funhouse sample game.So my two cents is that too cold or too hot is no bueno.I am all electric heat here(no natural gas available and propane is expensive) so a split unit would be my recommendation as well.
P.S. should add that this building has electric wall heaters and 55 is the lowest setting which is where they were set to.