I've found that my furnace works the best if I don't move my thermostat
around. It's about 5 off the floor, which is perfect for me. I tried
lowering it to 2 feet, but that was inconveinient, and I found that
sometimes mice (or the little tiny people that live in the fireplace,
not sure which) would play with the thermostat, which was fun for
awhile - but quickly just got plain old annoying. So then I tried
raising it to 10 feet; but then I needed a ladder to get to it.

So, to answer your question - don't lower your thermostat. Your plumber
put it where it is for a reason.