It looks like this has already been repaired once before. Note how your bad wire looks like it's "standard" PVC insulated electrical wiring instead of being high-temp wiring with a woven cloth insulation like everything else in your pic? That's a clue and may indicate why this has failed this time.
Those look to be simple, standard spade and lug connections. If you are able to make a solder joint or use a crimper, you shouldn't have any issues making up a jumper wire yourself.
- You'll need to purchase some wire that's rated for high temperature stove/oven use.
- You'll need to purchase the female lug connector ends that are the correct size.
- It's hard to judge from your picture, but you might need to purchase two different sizes.
- Pull the female connector off of the lug shown on the right of the first pic. (The one left behind by the burnt wire.)
- The 2nd pic shows a double connector at a right angle. I don't think you'd need to exactly duplicate this connection style. A standard straight-on connector should work, you'll just have to route the wiring slightly differently.
Your local big-box home improvement store might have the high temp wire you'd need to make this repair, so I suppose it's worth looking there. However, I'd guess you'd be more likely to have to go to either an electrical supplier or possibly an appliance repair place (do those still exist?) to find the proper wire. Call the closest electrical supplier and ask them if they have wiring appropriate for use inside a stove/oven. If yes, head on down and buy some. They'll probably also have a large supply of spade connectors and are likely to have the correct size. You may end up having to buy many more than you'd like, but you'll have them on hand for future use.
If they say no, ask them if they can recommend anyone who might have it. Most likely, they'll be more than willing to make a recommendation if it's something they don't stock and can't order in. Local places tend to want to be helpful.
Once you've got all your parts:
- Crimp one connector on
- You could solder, but it may fail using home soldering techniques in the heat around the oven. Check your solder for its melting vs working temp range.
- Crimp for a good mechanical connection then solder for a good electrical connection is probably even better.
- Slide that connector onto one spade end
- Make a nice run to the other connector to measure length.
- You may have to reroute the wire to make a nice loop, especially if you use straight on connectors instead of the 90° connector shown.
- Crimp the other connector on.
- Push both female connectors onto their male counter parts.
- Get to cooking.