In my experience when cars sit for long periods of time without being started the valve seals can get dry and will leak only on startup for about 5 to 10 minutes then once the hot oil softens them a little they will stop leaking. Blueish/gray smoke is indicative of oil burning. Black smoke is excess fuel and white smoke is of course water. If it is enough oil in the cylinders it will foul the plugs a little and of course make your car run really rough for a while until the oil gets burned off. As far as the heating problem I'm not sure about that one possibly the coolant temp sensor. Valve seals is a likely possibility though for the smoke.