Fall is the best time to aerate. I wouldn't do it when temperatures at night are regularly at or below freezing but your temperatures look balmy, now. I am assuming you have cool season grasses since you are looking forward to a winter and freezing, so go ahead and aerate. Leave those plugs right where they fall. They will disintegrate adding soil and bacteria to the surface that will greatly help with reducing thatch (if any). Core aeration reduces compaction and also gets more air into the lawn's bed to boost your micro and macro flora and fauna health.
By the temperatures you have shown, your fall is looking just fine for aerating. You are right to worry about subjecting the roots to freezing temperatures. Believe it or not, fall is the best time for aeration. Is this aerator rented or did you purchase your very own? (Make some money by helping your neighbors, aerating is one of the easiest lawn responsibilities).
Be sure you do not cut your grass any shorter than 3" at any time of the year. This length is critical to maintain always! The reason is, our cool season grass species that make up our lawns have huge root systems genetically. If you've been watering correctly (watering deeply and allowing to dry out before watering deeply again) those roots will be 4-6" deep. Necessary for making your lawn drought resistant and eliminating any weeds that might have germinated. In between watering the weeds won't be able to grow as the surface is dry and your grasses are enjoying moist soils down deeper. Also, the height of your grass at 3" (not 2 1/2" or 2 3/4" but 3") keeps the surface soils shaded further inhibiting grow of weed seeds and reducing evaporation.
The fall is also an important time to do the last fertilizing. The formulation is different than earlier in the season. Do not use a fast acting, high nitrogen fertilizer. You don't want fresh, new, more vulnerable grass photosynthetic matter going into the winter. This will set you up for major fungal disease problems in the sping.
I like the 'organic' (I am not a fan of the oft used words 'organic', 'natural'...chemicals are chemicals) brands that are extended release, slower to take effect, and come with bacteria for thatch decomposition and mycorrhizae (for symbiotic support of the roots). Make sure you look for the formulation for FALL. It will be lower in Nitrogen or at least equal in percentage to the Phosphorus and Potassium: For instance 7-8-9 or 10-10-10. Check out Dr. Earth...that is the one I am familiar with and used for client's lawns as well. Worth ever cent. You'll find this type of fertilizer is more expensive but by using this expensive fertilizer you only need to do 2 or 3 applications not the normal 4 applications. Follow the directions closely. It takes more fertilizer per application so it all evens out. I'd use this stuff if it were 3X more expensive!! Worth having the prettiest, healthiest crop of lawn you've ever seen!