Question about my Yong Heng Compressor “Digital Temperature Gauge”

I have a quick question about the “digital temperature gauge”. It came where I had to install this in myself so should I keep the wiring in the rubber band(nice and wrapped up so it’s not hanging), or should I take the rubber band off and let it hang(will it get too hot hanging and touching the insides)? At the end of the wiring, it has the metal tip where it reads the temperature. Probably a stupid question but I don’t know which is best? 
 
It's a thermocouple - the little metal tip is a joint between two different kinds of metal. A voltage difference sets up at that junction, and the size of that voltage depends on temperature. I think the best thing to do is keep it the same way, however you end up letting the extra wire hang. If you keep it coiled up (like I do), then always just keep it coiled up. If you let it hang loose, then always let it hang loose - otherwise you might change the temperature reading just by changing how the spare wire is hanging or coiled. Then again, we're just reading the temperature of the cooling water, so a reading that's within +/- 2-3 degrees is probably good enough. 
 
I noticed one thing about the OEM and aftermarket digital thermometers that I have..
Both of them would get a little wonky after enough time vibrating.. That said, I don't mount mine on the compressor anymore..
I plug it into comp head, and place the thermometer on a little stool a foot or so away, and in my case, it works much better.
Vibrations were causing it/them to turn off.. Not anymore..

When I mentioned aftermarket..

I got a Fahrenheit version from Amazon: https://www.amazon.com/gp/product/B073RP1476/ref=ppx_yo_dt_b_asin_title_o03__o00_s00?ie=UTF8&psc=1

Sam -
 
Because it is a Thermocouple the only part that reads the temperature is the end of the metal part. Be sure that it is snugly bottomed out in the hole. If it backs out a little bit and is not making contact with the bottom of the hole, you will not get an accurate temperature reading. It will read low, which could be a problem since we are using it to not exceed temperature.

Enjoy.
 
The digital thermometer arrives unattached and with a visible hole to place the thermometer case into. The problem is there is no visible place to put the thermocouple. Without taking the compressor case apart you only have the 2 options of letting the thermocouple dangle near the top of the case or to unwind the wire and let the thermocouple drop to the bottom of the case. Is there an better way to attach it????
 
The poster above is correct. A picture might help you but it isn't difficult to locate. Look on the back side of the black lower finned cylinder, the side toward the cover. You will be able to see a small hole in that black finned cylinder near the base. The metal part of the temp probe simply slips into that hole. No attachment, just a loose fit. It works well enough.
 
I noticed one thing about the OEM and aftermarket digital thermometers that I have..
Both of them would get a little wonky after enough time vibrating.. That said, I don't mount mine on the compressor anymore..
I plug it into comp head, and place the thermometer on a little stool a foot or so away, and in my case, it works much better.
Vibrations were causing it/them to turn off.. Not anymore..

When I mentioned aftermarket..

I got a Fahrenheit version from Amazon: https://www.amazon.com/gp/product/B073RP1476/ref=ppx_yo_dt_b_asin_title_o03__o00_s00?ie=UTF8&psc=1

Sam -
Does it fit well?