Thanks for your effort, but I'd really be remiss if I didn't try to give some extra tips so those tuning in here don't do so many things wrong. We always recommend buying oem electronic parts rather than discount parts. Way too many failures that makes it not worth the savings. This one in particular won't result in a breakdown, but could leave you without A/C in sweltering weather. That's bad enough for me.
Too bad you didn't have someone who knew how to solder to get one lesson from. It's really very simple when you know how, but your solder connections look less than proper. There are some decent tutorials floating around on the internet so as to teach you what to avoid.
Wnenever I splice wires or use butt connectors, I always try to stagger the connections so as to minimize the possibility of shorts if the unlikely failure of insulation happens. Cuts down on the huge bulge effect at one point in the wiring too.
Sensor end should be completely in free air rather than taped against any other object which might affect the accuracy of a true temperature reading.
After decades of experience, electrical tape has very little application in real life for me. I've seen very few instances where it didn't ooze and unwrap to look pretty messy and unprofessional. Especially unsatisfactory in wrapping around strands of wires.