York upflow furnace - flame sensor issue?

This sounds to me like the filter needs to be changed. The burners may be shutting down on over temp. Cleaning a temp sensor should be done very carefully with a brand new piece of scotchbrite. If you don't know what you are doing you could ruin something expensive. Call a qualified tech.

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York Flame Sensor

It sounds like the flame sensor does need cleaned. It is located between burners and heat exchanger. There should be an ignitor on one side and the flame sensor on the other. Be sure to turn off the power to furnace, remove the screw holding flame sensor in place, remove flame sensor and clean with a brillo pad or scotch bright pad or brass brush. Re-install and the furnace should be fine. This should be done annually to prevent unexpected shut down.

I recently had a similar problem . Mine turned out to be a flue obstruction. (a bird got in the chimney)

Flame sensor will be in the combustion chamber . Some have a combination igniter and sensor. It senses if the pilot is lit. 30 minutes seems like a long time to run with a bad sensor.

Turning off the power switch resets the system.This is why it runs after you turn it off.

This sounds like what Polar Bear said-an overtemp issue causing the high temperature limit to shut the burners off. He's correct, check your filter first amd replace if needed. Also a dirty blower fan or a dirty evaporator coil (if it is a central air conditioner) can cause this. The 2 I suggested are more a service tech type of issue, unless you are familiar with furnace fans and cleaning A/C evaporator coils.

Good Luck

30 minutes is a long long time.The blower will turn on with no flame to remove any remaining heat.If it runs for 30 minutes and your house isn't warm you better call someone to look at it.