How would I find out how much electricity (volts, amps?) a typical electric blanket uses in a four hour cycle? And, how would I figure out how to provide this power using a rechargeable lithium battery? What type of battery could provide the necessary voltage/amperage for this four to five hour time period?
Look towards low voltage electric blankets. They make them. As to power use? Measure the voltage and current over the 4 hours and average it. Once heated the current will drop off. Obviously the size matters. King and Queen will use more power than a twin or full. There are simple devices like the "Kill-A-Watt" that will tell you power consumption of a device. However, start with low voltage electric blanket which gets you to units like this where later the power supply would need modified. You really haven't provided much information.
Doesn't an electric blanket have a thermostat that turns it on and off depending on the setting and the ambient temperature? Then it uses NO power each time it turns off.
Certification agencies insist this correspond to maximum power under normal load. So even if it's 1000 Watts at a 10% duty cycle = 100 Watts average, it still gets rated at 1000 Watts.