Changed battery on my 2008 Polaris 500 now hot lite comes on and cooling fan runs constant even with key off?

it will run till reaches cool down temp safety feature

The fan is built to run if the engine is hot. You will need to clean the cooling fins and radiator.

Check the main fuse to the ignition switch.It will either come directly from the battery + terminal or pick up from the "hot" meaning "positive" side of the starter motor relay. If it comes from the relay you will locate it by following the main "positive" lead from the battery. From the relay you can then trace it to the main fuses. Hope this helps you out.

theres two sensors one in the rad, and one in the left side of the jug

The fan will only run when it needs to. It's on a sensor. The only time mine comes on is if I'm hauling something

51 is a injector on #1 cylinder is stuck open.. will need to check wireing for damage first. 52 is cooling system fan issue.. fan is overload condition or maybe shorted to ground. Will likely have to chase wires to find issue.

I have a 2001 polaris sportsman 500 H.O. I have replaced the fan and the thermial fan switch,and checked the thermostat. Everything is either new or works there are no bubles in the coolant when its running I am running out of opptions . If I unplug the thermal fan switch and plug a jumper wire in the fan will run. I thought the new switch was bad and I tested it and it is good

Does the cooling fan ever run when the engine is hot? If not, you may have a problem with the fan thermostat.

For the record, spray carburetor cleaner does no good if it's sprayed on the outside of the carburetor with the engine running. That's not what it's for.

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prob needs a new thermostat