The FBH will have nothing to do with blue smoke out of the exhaust, unless you mean the FBH's small flue pipe?
Blue smoke at start up can be down to several things. Oil in the inlet tract is a common cause. This is drawn from the turbo but seems to show mostly on starting. I have a similar problem on my TD4. I'm planning on cleaning the entire inlet tract in the summer.
The FBH will run if the air temperature is under about 5°C , the coolant is below 72°C and the engine is running. Unless you have a separate timer or remote control for it.