I think what this author is asking is relatively simple. How to measure (observe) the current capacity of a wire around 16 AWG gauge with different insulations in ambient conditions.
From what I remember, such an experiment was made in an episode of DIY network's Deconstruction to compare copper wires to aluminum wires. To actually melt the copper wire, (if I remember well) it took quite some current and was provided by a welding power supply. In your case, if you're only melting the insulation, you won't probably need that much current. Remember to perform this experiment in a safe environment, since toxic fumes will most likely be released and there's always a possibility of starting a fire. Also, remember that you are dealing with thermal time constants, so heating the cable with a very fast high-current spike is different than heating the cable with a dc current (or 60 Hz AC).
M.