I think the general consensus is this isn't a great idea. However if the stove is a jenn air model as mentioned above, with the stove knobs on top of stove it may be ok. I wouldn't let it cover the whole cooktop, just the vent area.

You know...I have no children at home, either, but I just do not think putting any kind of fabric covering over a cook-top is a good idea, at all.

If the vented air goes down, it is an emergency outlet for gas (which is heavier than air and would spill down)
So, what we are talking about here is blocking the escape vent, which means that, if someone knocks the knob on, the gas will fill the kitchen.
Crazy.

The OP never said whether the cooktop in question is gas or electric, or even that it is a dowdraft model for that matter. It would be a whole lot safer any way you look at it , to simply make sure the venting is properly insulated and to possibly clean the gunk out of the outer wall vent opening where accumulated grease and gunk may be keeping it from sealing tight when not in use. http://www.freesmileys.org/smileys/smiley-forum/2c.gif

Wow never heard of such a deal. I bet you could be making the very first stove quilt.lol

If your sister never, never, ever, uses the stove, she would be ok with taking out the fuses or turning off all power/gas to the device? That's the only way I could ever see this happening - or just removing it and replacing it with cupboards.

I bought element covers for my stove at one point - quite sure that I would never turn on the elements accidentally. Guess what - it happened. Luckily I was right there and turned off the burner in time - the cover was burnt but no other damage. There are just soooooo many things that could go wrong.

I have an old CorningWare cook top and love it and wouldn't think of putting anything on top of it that might burn. The vented hood may be able to be done outside of if you can plug it. There is a vent in the upstairs bath and we can pull a plug and use something there but it never bothered me. I am alone but have frequent visitors and those darn knobs are on the side of it and if they brushed against them with a casserole or something...I don't like that idea at all. I think if the vent became a real problem I would just try to tape it...on the outside but I cook too much and the steam has to go someplace.

I think I understand what she is wanting to do. If she has a Jenn Air like mine, it has a center down draft to the vent outside and cold air does come back thru it in the winter time. If she laid the top over the vent only it would help and wouldn't be touching any burners or cook top. I have used a manilla folder over the filter down in the down draft in the winter, but you must remember to take it out before you turn on the fan to take the cooking odors and grease out of the air while cooking. It doesn't touch the burners anyway shape or form, nor is it close to any of them. It lays on a metal filter that catches the grease etc. If you don't take it out when you turn the fan on, it doesn't pull anything out and will eventually burn your fan motor out. If you closed the vent from the outside, you couldn't use your fan to take the odors etc., out.

Sorry, I just don't see why anyone would do this

I've made a couple of quilted tops for my induction range top and have been asked to make them for friends. Induction cook tops are always cool unless a pot with iron content bottom comes in contact. I can place my hand on the element immediately after removing a hot pot and the element will be off. Quilted tops are excellent to cover and protect your (cleaned) cook top. Whenever there's a flat surface in the kitchen, someone wants to put something on it - groceries, dishes, toys, you name it. The quilted cover protects it from being scratched and looks pretty too.