Why are these wires getting hot????

Not showing any resistance meaning a short? Zero ohms? And then unplugging it meaning infinite ohms?
Zero ohms is interpreted as hot for a thermistor which I suspect it is. Infinite ohms would mean very cold then and your data of starting and running would seem to support this.
It would run pretty well then if we put around say maybe 600 to 1000 ohms across the two wires...maybe less...as low as 200. Wild guess.

Electricity was never my strongest subject, but I get zero ohms When I test the sensor after i removed it. I tested the other end of the plug that's attached to the bike and I got 1.4 ohms of resistance with the bike off And 5.88 with the bike on.
I'm not sure that it matters how much resistance I get on the other side of the plug, I'm thinking it's just what's the temp sensor itself reads right?

I just checked the continuity between both plug tabs and and the temp sensor at the other end and I got nothing. Wouldn't that mean that the wire maybe broken somewhere along the line?

Right. Measuring the plug resistance toward the engine is meaningless except to find out that it is connected to something on the far end which is good. So the sensor itself is shorted showing zero ohms. That's why the gauge shows hot. And it is most likely a thermistor which generally has a negative temperature coefficient (resistance gets lower as the temperature goes up).
FYI if it were a wire or carbon resistor used as the sensor, the resistance would go up as it got hotter. That's a positive temperature coefficient temperature device.

There's a good chance that that is what is wrong with it. I would look for a wire break at the place (s) where it was clipped or tie wrapped. BMW has a reputation for cutting wires with excessively tight ties. Measure the resistance across the plug and while that is hooked up, push the wire together, wiggling it, at places along the length of the wrapped wire. That will often show you where the break is if it is a break.

Roughly 2.8k @ 20C.
It is a NTC thermistor

So I really wanted to ride in the awesome 80 degree weather so I stopped by RadioShack and picked up some 1.5k ohms resisters. I twisted 2 of them together, stuck them in the plug where the sensor was and the ole girl fired right up! The temp gage was relatively in the center, but fluctuated around a bit but Didnt seem to cause much of an issue today. I wouldn't take it on a long trip like this but it sure as nice today!

Amazing what we do just to go for a ride huh?

The new sensor arrived, but it still has some issue starting. it cranks more than normal....???? I wondered if I had not put a fuel line on correctly, so I checked and twisted all the connectors. Once the bike warms up it seemed to run fine. at one point the new temp gage was fluctuating quite a bit. I unplugged it and re-plugged it and it seemed to stop also. Ill try again tomorrow morning with a cold engine and see how it starts.
any suggestions as to what else I could have done in the meantime?

by the way, I did install a resistor and drove it once, but it didnt run very well and still have a hard time starting, so i parked the bike so i wouldnt burn the starter. Nothing else was messed with. frustrating

The Temp sensor had resistance so Im pretty sure its not that....

I traced the hard starting down to my fuel injectors. They don't seem to be getting any power. I benchtested them and clean them both but when I put them on the bike and have them hanging out they do not Spray fuel when the bike is turned on
Any ideas

I take it you mean they don't spray fuel when the engine is turning and not just switched on?
Get an LED and a resistor (a scope or frequency meter will work better but I doubt you will have one of them), connect it across the FI plug (bike end) turn the engine over and see if the LED flashes consistently. If it flashes ok then start to look at your fuel pump or the controller. If it doesn't then something else is wrong. I highly doubt both fuel injectors went bad at the same time. You are really getting into the realms of something like a GS911 or the dealers diagnostic being needed here. It will save you a huge amount of time fault finding.