I keep tools in my shed with little issue in MA. Only real issue with rust is when I need to work in inclement weather and don't dry them (snow or rain). Been out there 6 years now with little issue. I also keep a socket set and bag with assorted tools in the toolbox of my pickup all winter...
If you have an issue with rust in the garage I would expect it's related to moisture not temp. My basement has moisture issues and I have the resultant rust on things and mold on leather goods.
Try wither solving the moisture issue or adding a dehumidifier which will also add some heat.
May want to look at: Are you insulated? Moisture barrier intact? Is there a noticeable water leak from building, internal plumbing, or ground water? (I have ground water issues when it rains coming through my stone foundation) interior spacer of the house not vented into the garage? I'm on a well which leads to lots of sweat on pipes, we have a thin floor in the basement and grading outside needs to be changed to help keep rain water away from the foundation.
wiping your tools down with a very light coat of oil (fluid film, wd40, 3n1, even motor oil) will go along way to protecting them even in poor storage conditions.