Check for sings of it leaking. Check the weep hole especially. Doesn't sound like a WP to me if the car has coolant and isn't loosing any. Also could be a stuck open or closed thermostat. Trying flushing the coolant system to see if there's air in it, Get the light scanned and tell us what the code is. Running rough sounds like a misfire and smoking can be a head gasket which would contribute to the misfire.
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