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Hello yes there is an engine coolant temperature sensor. It sounds like you probably have a fuel injector leaking down after the vehicle sits and the engine is burning off the excess fuel on first start up of the day. A fuel pressure gauge can help confirm a fuel pressure leak down. Also if the vehicle sits often, the fuel quality may also be an issue, these fuel pumps use a sock that will degrade in the fuel tank and possibly cause a loss of fuel pressure under a load.
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Is there a concern with exhaust smoke upon the first engine startup?
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