Ok here's a better update to my last.
I used Kenneth Shirriff's Infrared Libraries, with my own definitions to recognize this protocol, which correlates well. I think Mr. Shirriff had this kind of stuff right on!
Here's what I did:
I found that multiple different hexadecimal or binary values represent the same displayed temperature value, which means to me that there's some decimal places in this temperature value. The m_neg, and m_pos variables I came up with through some more linear regression. It's not perfect but it's "dialed in" pretty close. I've been stuck on regression lately. Lets' use regression for everything!!!!! Okay never mind.
Watching the hexadecimal values, I found that the "F" hexadecimal place, just after the sensor ID value indicates a Negative temperature value in Celsius, based on my output.
LAN_Temp.ino (4.51 KB)
IRremote.zip (41.4 KB)