Chevy silerado 2013, prompt came up saying engine hot a/c off

Faulty temperature sending unit or faulty gauge?

Replace the temp sensor

check the that wire to the temp sender unit is not shorting out as it will read hot if it is remove the wire and if the gauge goes back to cold then replace the sender unit.

Take to dealer and use your warranty.

Watch the temp gauge when the electric radiator fans come on. The temp sensor that controls when the fan comes on may be faulty.

It could be several things. The fan relay may be bad, The fuse for the temp. gauge could be blown, or the temp sensor could be bad.

have you changed your temperature sensor

bad gauge or bad thermostat.

Fans come on because when you disconnect, it goes to default mode of fans on high speed.

check the coolant temp sensor

When you say "red hot" do you mean actually glowing? If so, you'd have serious trouble. If you mean only hot to the touch, that's normal - these engines run pretty warm. And yes, the gauge in the center is normal - the OEM temp gauge is a dummy gauge, only meant to show you that it's either cold, overheated, or mainly OK. Use your oil temp gauge as your main indicator - at least it's graded numerically and you can actually see the oil temp.