Temperture gauge show's hot after a one minutes running

Where is the temperture gauge Colin, RE POST make model # and your complete question, so we at Fixya can answer your question effectively.
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the temperture sending unit needs replacing.

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The guage itself is probably bad. Maybe try replacing the guage or instument cluster with a junkyard one.

Defective coolant temperature sensor if it reads hot as soon as you start the engine. Check the wiring before replacing. The gauge itself can also be bad but not likely. The temperature sensor will look like this.

temperture gauge is not working and dash sign comes on says turn off e/c e/c is on , but the temp gauge doesnt work

you blew the head gasket...

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Remove the temp sensor wire with key in on position to see if it still goes to hot position If it does you have a short in the sender wire and if it drops to not reading the sensor is probably faulty

First of all, it doesn't sound like your thermostat is working correctly to keep good hot/warm air coming , so I would change that, or have it changed for better heating inside. If you lift the hood & look in front of your radiator, On the engine side, you'll see a fan attached to, or in front of the radiator. It won't come on until the coolant temperature gauge gets up to proper operating temperature. Without getting in to too much detail, have your thermostat changed, and my guess is everything else will start working as it should, and whoever does the work, should know enough to check the fan operation when they do the thermostat.