Code P0113, the temperature gauge stopped working and the fan keeps running?

The P0113 code is intake air temperature sensor failure. I would drain and fill the cooling system while you are doing the job.

https://www.2carpros.com/articles/coolant-flush-and-refill-all-cars

I would try the engine coolant sensor first because it might affect it. Here are the locations for both, so you can change them out. Check out the images (below). Please let us know what you find. We are interested to see what it is.

Thanks a lot Ken!

It’s very helpful!
I will replace the coolant temperature sensor and IAT sensor. Yesterday’s code p0113 changed to p0116 when I detected it again today. And the temperature gauge was down to bottom no movement, two radiator fans moving endlessly while outside temperature about 60F. And RPM at neutral surged to1,700 RPMs. It’s more difficult to fix now.
If coolant temperature sensor and IAT sensor bad, could it cause the issue? Thanks for your further comments and instructions!

Hi Ken, Thanks a lot for your instruction and diagrams! I replaced coolant sensor, intake air temperature sensor (IAT), TSP sensor, and thermostat. And rpm return normal from 2000 to 750. P0110 code now Was cleared automatically, desk board thermometer gauge recovered to normal, coolant fan also recovered to normal. But when refill coolant, open radiator cap, startup engine, air and coolant flow out from cap endlessly, and air coolant tube create much air. The right bleeder burst out of air, then ant coolant, but left bleeder no coolant but air. What can I do to refill normal coolant and air bleeding?

It sounds like you may have a blown head gasket. We should follow this guide to double check because if it is the problem we are having can be caused by this failure. You can rent the test kit from the auto parts store for cheap.

https://www.2carpros.com/articles/head-gasket-blown-test

Please go over this guide and report back.