Time to get the radiator off for a clean, it is most likely clogged with dirt at the bottom. Common problem on the k13 engine. Fix it early on so that it doesent get damaged and need replacing. the take it as standard work to clean it at least every 2 years.
My current K13S got all radiator pipes (rubber) replaced at the last service before i purchesed it two years ago, it keeps the temp low as expected and especially when the fan kicks in in hot stands/low speeds.. the fan goes off after a while, means that it cools the liquid as expected.
My previous K12S had some cooling issue, but not that severe - it cools properly when in decent speeds, but when the fan kicks in it did not goes off unless going back to speed that wind will be decent.. one more issue - chack pressure in the system, my K12S had lost of pressure from the cool liquid reservoir tank cup lid, it did not hold pressure properly.
Oh, anoter thing - once in a while clean the radiator - from the outside: spray water with little soup to clean the dirt that stuck in between the aluminum leafs.
Good luck! .. keep in mind that engine cooling properly will operate & live longer