I have some nichrome wire, some kapton tape, and an available arduino. Probably I don't want to make a blanket, because that would be a little too dangerous... But I could at least make a foot warmer or something.
I'm trying to think of a good material to use for the heating pad, something to sandwich the nichrome between.
Use extreme caution when attempting this. You have a couple of hazards which could prove deadly, or, at least, extremely painful if something goes wrong.
I'd recommend running such a device from low voltage, and have it isolated from the power line (e.g., isolation transformer). The temperature of the wire could easily melt through most common insulating materials, allowing the user to come in contact with either the (thermally and/or electrically) hot wire.
I believe (but, please don't take my word for it; investigate this yourself!) that commercial devices use a high temperature Silicone rubber to insulate the wire. And, usually, a couple of layers.
Also, there needs to be a way of measuring the temperature of the device so that it doesn't overheat and either melt through the insulation, or start a fire (It's not good to burn down your user's house, especially with them inside!). One way of doing this is by dynamically measuring the resistance of the heater wire. Since the resistance of wire changes with temperature, by measuring said resistance change, you can get an idea of the temperature of the wire. It requires some pretty fancy electronics, but it can be done.
Personally, I'd scrap the nichrome wire and use power resistors. Dale (Vishay now) used to make some high power resistors which would be bolted onto a heat sink. A couple of these bolted onto an Aluminum plate should make an excellent foot warmer.