Martik wrote:

Heat element burnt out near the terminal so I rerouted and crimped it back
on and bypassed the blown thermal fuse with a 1/2" length of 18 gauge solid
copper soldered to the remains of the fuse leads. There is a bimetal thermal
cut-out in series with the fuse. Is this adequate protection without the
fuse?

No, no, a thousand times no!

The remaining one will be the thermostat. Replace the
thermal fuse with another; they're inexpensive.

Ken.