YTA for this opening line alone-I'm the breadwinner and manage our finances and pay for everything in my home.

Who cares? That doesn't make you the final word on everything in regards to your wife, who you married, who co-owns everything with you. Letting the heat run a little more is no big deal, and if it winds up being that much of a burden on the household, sit down with her and negotiate how to split the bill without demanding she just pay because you pay more.

Don't use money to judge your usefulness vs someone else's. She has just as much value as you do, and while your feelings on this matter as well, hers shouldn't be brushed aside because you think you have a better solution. It's just turning on the heat on, it's not a big deal and doesn't warrant emphasizing your status as a working person in hopes of swaying opinion.