The birds can also sit on the edge and warm up a bit. Yesterday, I had five crazy little sparrows all taking a group splash together -- it's good to know that my work is being appreciated. =D
All you need are the items listed in the photos, some left-over insulating bubble-wrap, some silicone sealant-adhesive, a little "Great Stuff" spray foam insulation, and some grey/black/brown paint. Amazon has the bird-bath items and Home Depot has all the rest.
Here's the gist of how I made it:
1) Press+bend the heating element to conform to the back of the metal bird-bath
2) Bond the heating element and bird-bath together with four quarter-sized dots of sealant toward the edges at the 12, 3, 6, and 9 O'clock positions
3) Cut a piece of insulating bubble-wrap about 1" larger than the diameter of bird-bath
4) Turn the bird-bath + heating-element upside down and hold the bubble-wrap to the back of the bird-bath, then cut away the excess bubble-wrap, leaving about 1/4" of the bird-bath showing all the way around the edges
5) Add sealant along the back of the heating element in an 8-spoke criss-cross pattern
6) Press the heating element and bubble wrap together, with the bird-bath upside down and the bubble-wrap facing up. Weight it all down with a bag of bird-seed plus any additional weight you may have on hand on top of the bag of seed (because the bag of seed on the bottom will conform to the shape of the bird-bath to help the bubble-wrap bond more closely).
Allow the bond to set up overnight; remove the weight.
7) Add more silicone sealant-adhesive all the way around the edge of the bubble-wrap to form a water-tight seal.
For the base, I used an off-the-shelf oval-shaped granite (real stone) bird-bath.
To keep water from gathering between the granite and the heated bird-bath I lined both parts with kitchen plastic wrap, sandwiched them together, and sprayed "Great Stuff" insulation all the way around the edges. The next day I used a sharp knife to saw away the excess insulation to make a nice conforming edge between the heated bird-bath and the stone bird bath.
Finally I masked off the heated bird-bath and painted the insulation with grey/black/brown paints to create a faux rock look.
In the summer I remove the heated bird-bath and just use the granite stone underneath.