Convection...sounds like you may need a working check valve. Well, it would be good to get rid of that tankless coil as it is not very efficient and can be limited in the hot water supply from it. To be able to make hot water at any time, the boiler basically will run 24/7 between its min/max aquastat settings. Hot water rises, and if there's no check valve in the system, it can flow around the loop. Since it isn't being pumped, it doesn't flow very fast, but it is continuous, even in the summer when you probably don't want the heat. This may be one reason you haven't needed to turn up the thermostat...you're getting some heat, regardless.