Iron sheets? WOW. I know my stepmother used to iron pillowcases, but never sheets that I recall.
I iron neither, but I use flannel sheets year-round. (Even if I didn't, I wouldn't iron.)
In fact, I would be hard pressed to find my iron (I have one, but I don't use it).
I take my clothes out of the drier ASAP, and have a lot of Citiknits clothes for travelling, and they are no-iron. I also don't wear suits or blouses per se, but mostly knits.
Just think of how much energy one can save or waste depending on if they iron or not. (And ironing sheets is a big waste of energy, IMO. May be just a little bit at a time, but it still adds up).
I used to have a roommate who would heat up her iron ever single morning, and iron one outfit at a time, that she was wearing for that day. What a waste, I say.