Can you post the make and model number please.
Also does the grill and the oven still seem to be getting hot still?
Ok usually when you get white smoke its one of the elements is failing. If you inspect the grill element when you can you may see signs of burning on there were the element starts to split.
If the grill looks ok then remove the back cover and inspect the fan element as well. As from the sounds of this its going to be one of the elements have failed or its ready for blowing.
If you find next time you use the oven or the grill and you find its not getting hot then the element for that part has blown and will need to be replaced.
So for the white smoke you see im afraid this is the sign one of the heater elements in there has blown or is ready for going.
If you need anymore info just get back to me.
Not sure what you mean about paying anymore as you only pay the one fee which you agread to when you asked the question. You dont pay for each reply its just one payment for as many replies you need on this so dont worry about that.
As to what you said about your son using it. Then it sounds like the grill element is the issue here, You will find the grill has either fully gone of its about to fail. So you need to replace the grill element to fix this fault.
I see the question is still open, Do you still need help on this?
If so just get back to me but if not then if you could rate the answer that would be great.