I'm planning to lower the water temperature to discourage my wife from taking long showers.
That sounds a bit passive-aggressive.
She wastes too much water and I want to see her naked.
It's wrong to tamper with a water heater without informing the people living in the house. If you mess up you can burn and injure someone.
It's fine, she's such a hot tomato, it wouldn't hurt to cool her off a bit.
You're both adults. You need to discuss your plan to lowing the temperature and financial reasons why you're doing it. I'd leave out the "hot tomato" angle.