So I went ahead and bought some of these and tore down an extra one. Inside is a single sided PCB with a blob top IC. Part of the blob was covering two pads marked F° or such indicating it is the control connection for F or C. I bought F's so if you want to change best get a C so you can remove the jumper.
However, you need to be expert at realigning zebra strips to get the LCD to work once more.