steaming pipes
I assume the smoke is white.
Being the smoking is getting worse as the motor gets warmer and you are not loosing water/coolant is sound like you have some diesel in your fuel. Either someone is playing a joke on you and put some diesel in your car while you were getting your motor built. Or you bought gas recently and the tanker guy put diesel in the ground and now you have it in your car.
Diesel in gas in a gas motor smokes white and as a motor gets warm it smokes more because diesel is an oil and when it hits the hot exhaust system it really smokes.
Take a gas can and hook it to your fuel pump and run your motor awhile and see if it clears up. Your fuel can still smell normal and have diesel in it.
Just about all new motors run a little warm because of the added friction/tightness.
Chuck