When not up to temperature is where the problems exist

HI.

My Audi A3 2015. When first on start up it ticks over at 1100 revs. If I turn the car off then restart it ticks over at 800 but then gradually raise up to 1100 again. If I try to push it a bit under the full temperature it goes into limp mode where I turn the car off and turn it back on and clears limp mode unless I push it a bit again. When up to temperature it works and boosts perfectly fine. to me the fan is also kicking in to much as i've not travelled soo far for it to be kicking in. I've also noticed it smells hot when ticking over at 1100

Any ideas? 

Cheers