BMW E46 316i Choke/Heat problems

[Longitudinal4Cylinder]

this will probably be one of the stupidest things you've heard of but oh well, One day i started up my car. i realised the auto choke isn't working because the revs aren't higher and the coolant temp is rising very slowly. You may be thinking a faulty thermostat but it doesn't overheat.. And it still warms up fully. And this is where the 2nd problem (maybe not a problem) pops up. the coolant temp gauge shows a tiny bit over the middle. Imagine a clock, it's in the 12 and a quarter position. it stays there even though im not driving hard. it done this last year but only during the colder days in winter, but the choke still worked then. So i asked this on FB and ppl said it would be the thermostat housing temp sensor. so i went ahead and bought it. i am going to replace it on monday hopefully and that should fix it. before you say "omg 4 pot lol", just keep in mind i can't afford one yet and this here 316i is perfect and never gave a fault/code in a year. Also the secret menu 7.0 engine temp is a bit dodgy as today it was doing the overheat thing and it said 70 degrees celsius so idk. But once it said 115 when the gauge was spot on in the middle. Please any help would be appreciated thanks.