A lot of the small ones (BS170, for instance) are generally about 1.5V (Specified 0.8V to 3V)You need a low Vgs(thres) MOSFET to minimize the total voltage drop across the limiter.
A schottky diode in series with R2 will deal with the temperature compensation, giving I = 0.4/R2. The compensation has made the current less exact, but more stable!