smoke from engine

My son's 1997 Honda Civic SI manual transmissinon in perfect condition is parked in my driveway for about seven months. About three months ago I started it and ran it back and forth in the driveway ( it is presently unlicenced and uninsured ). The battery was in it all this while. I took out the battery about two weeks ago and placed it inside the house ( outside temperatue in Toronto was/is below freezing ).
Last Friday ( 30th Nov ) I put in the battery and tried to start it - the hood/bonnet open. I noticed a little smoke coming from the left hand side ( driver's side ) of the engine - that is the side opposit to the battery. I waited a few minutes and tried again. I saw more smoke coming from the same place of the engine. When I got out of the car to see/smell/pinpoint the exact location from which the smoke came I could not determine.
What component could the smoke be coming from and what could be the cause?
Thanks.
Ghelp

 

It could be oil from the valve cover or some other source settling on the exhaust manifold and burning when it gets hot due to start up.

 

My wife's 93 prelude had a leak in the exhaust under the hood somewhere. Never bothered to investigate where because the timing belt broke shortly thereafter and scrambled the engine.

 

Please note from my post that the temperature is below freezng and also the engine did not turn over to heat the exhaust manifold. I am thinking that it is more like electrical shorting - I do not know.
Ghelp