Nowadays, most folks just use a hot water bottle to keep their feet warm.
But beware: if they are too hot, they can cause severe burns, which is why hospitals have temperature controlled wet heating pads.
the “bed warmer” was placed in the bed or passed over the sheets so that the sheets were not ice cold when you got into bed. It was not left in the bed.
as for hinges: most of them seem to have a simple single hinge...
You can buy some on ebay.
It’s not so much the hinges as the placement on two equal parts like tennis rackets places next to each other the swivel close to 360 degrees.
Forget the bed warmer.
The bed warmer part was more for the roundness. I didn’t realize that the top was attached with a different design.