All along, I've been planning to use BMP280 sensors for temperature on this project. I have quite a few BMP280 breakout boards laying around unused. I got a few of them before I realized I could get BME280 boards that also detect relative humidity. I got a bunch more because when you try to buy BME280 boards from random overseas sellers on eBay, you stand a good chance of receiving BMP280 boards instead.
Anyhow, any temperature sensor with an I2C interface can work pretty easily with the rest of the design.
A funny thing happened. OK, two funny things. When I first added a BMP280 to the breadboard, I had some kind of brain glitch and wired it's Vcc to the 12v supply instead of the 3.3v supply. No smoke came out, but that little board was completely dead by the time I figured it out. I grabbed another BMP280 and wired it correctly on the breadboard. It worked, except it was reading a temperature of 189 C. I've never seen that behavior from a BMP280 or BME280 before. I don't even know what could make it happen. I popped it out and replaced it with a third BMP280, and things worked as expected.
So, that was weird. I'll remember to include a step for sanity testing the temperature read-outs when assembling things.