When you work in an old building with HVAC issues, I find that layering is a MUST. There is virtually no temperature control in my 100-plus year old school building; a day that is 70 degrees and cool outside can feel like 85 degrees in a hot classroom without ventilation. You walk into another classroom, and it feels like 60 degrees. It's impossible to predict, so all one can do is prepare.
I've been layering clothing quite a bit to adjust to the temperature issues. And although I have plenty of fabulous cardigans and blazers, I don't have too many shells and sleeveless tanks. I was able to pick up quite a few good ones recently from Old Navy.