You have a EXT. The mixing valve is bad. You can remove it and attempt to clean the minerals/calcium out of it or replace it. So, yes, you are right. It DOES mix with the cold water thru the mixing valve. 160 degree water mixes with cold water thru the mixing valve to produce 130 degree water. Doug
PS, you do NOT have a 16 gallon Water Heater. You have a 10 gallon water heater that mixes the HOTTER(160 degree) water to produce 16 gallons of 130 degree water.
https://www.amazon.com/s/?ie=UTF8&keywords=atwood+mixing+valve&tag=googhydr-20&index=aps&hvadid=241901783643&hvpos=1t1&hvnetw=g&hvrand=297869772489756071&hvpone=&hvptwo=&hvqmt=e&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9027307&hvtargid=kwd-325735003851&ref=pd_sl_5u7krd5h8s_e_p37This is where it is located.
https://www.amazon.com/Atwood-94026-XT-Water-Heater/dp/B000HDCRH4/ref=sr_1_5?ie=UTF8&qid=1539475468&sr=8-5&keywords=atwood+mixing+valve