Reading the book, I was disappointed to see that re-instituting Fahrenheit was not considered. The scale was actually created to be easy to make in the lab!
1. Take ice water (ice created using a freezer from Chapter 4) and measure its temperature. Mark this number 32.
2. Take the ice water and add ammonium chloride (which you get from mixing hydrochloric acid and ammonia, Chapter 5) and add more ice until it's as cold as you can get it. Mark this number 0.
3. Use compass (the drawing kind -- I made another post on compasses and drawing accurately) to take the distance between 0 and 32, and mark 64, 96, and so on.
4. Use the compass and straightedge to bisect the line between your points -- 16, 48, 80 -- and keep subdividing between them. (This is why it uses powers of 2.)
5. Test your thermometer by taking your temperature! It should be close to the 96 mark!
In the absence of refrigeration technology, you can simply measure ice water in winter (using that as 32) and assume your body temperature is 96 (instead of the more accurate 98.6). If you haven't gotten to the point to create refrigeration and ammonia, then you probably don't need a more accurate thermometer.