GBM writes:

Is there a way to do this without any expensive instruments?

(If this is DC power you can't use a clamp-on meter as some others
suggest.)

If you're trying to measure duty cycles, you can improvise a cheap logging
meter with an inexpensive multimeter from Radio Shack (etc) that has a PC
interface, and a laptop or other computer. You can even simplify by
omitting the computer and just pointing a video recorder at an ordinary
meter, and fast-forwarding through to find the on and off times. No need
for expensive logging instruments for a one-time procedure.

Adding insulation is not typically an improvement in anything of recent
construction. That's a fantasy factoid lingering from the 1970s energy
crisis, endlessly repeated by people who've never measured the realized
benefit.