I have transported my helmet on Swiss, Air Canada, and Air France, without anyone raising an eyebrow. Like Grant said, just put it in a duffel bag or bowling ball bag or something like that. Things might be different if you are taking a flight to, from, or within America - the security folks in America are much more twitchy and jumpy than elsewhere in the world.
As for the heated vest, I wouldn't suggest you wear it, that's for sure. I think you could probably take it on as carry-on baggage, but it would be best if you passed it through the x-ray machine in its own plastic bag, so the staff could see exactly what it is. Once they have a second look at the x-ray, they will see that it is harmless. The first look, though, might surprise them, so it might be a good idea to tell the person who puts it through the machine what it is, before they have a look at the picture. It would probably make the whole process easier if you could bring along a brochure or catalog from the company that made your heated vest, something that explains what it is and shows pictures of it. Chances are that the security screeners will never have heard of such a thing before.
Obviously, it would be better if you could pack the heated vest in your checked luggage. I normally pack mine in the saddlebag of the motorcycle, then ship the whole darn motorcycle as air cargo.