How can I repair a chewed-through power cable?
By all common sense you should not try to splice an appliance cord to make it longer. What you should really do is to open up the appliance and remove the remaining chewed off chunck of cord. This may require you to free any type of cord retainers and / or strain reliefs. 

Then a new cord of ratings same as the original should be installed in place of the old one. It can be very handy to purchase a ready made extension cord that has nice molded ends on it (rated properly of course) and cut the socket end off of it and use the remaining part to wire into the heater. 

Sometimes you will find that inside the appliance the wires may be attached with some type of crimp on terminals. These types of terminals are generally available at hardware stores but if you cannot find exactly what you need check online at retailers such as Digikey or Mouser.