Just last week I ordered a thermal fuse from this site and replaced it, per the thread

http://forum.appliancepartspros...ot-start.html#post791555

Since replacing the fuse one of the blade connections on the heating element is getting so hot it is burning through the wire. The bottom of the two blade connections for part 17 (Bulkhead parts for Whirlpool LER8648PW0 - AppliancePartsPros.com) heating element is getting so hot that it burns clean through the wire. I initially thought the wire had just gotten brittle and broken off so I clipped it and moved the clip down to clean bare wire and reconnected it. When I turned it on after doing that I watched it and it started to heat up, as the heating element heated up the connection started to get so hot it was glowing and burned through.

If anyone has any thoughts about what might cause this I would be most appreciative.

It sounds to me that you have repaired it correctly so I do not think my input will be of much use to you but here it is.

First I would check for a grounded element.
Remove both wires from the heating element and check it with a meter, should be 8 to 12 ohms.
Then measure from each heater connector to the frame, be sure to get to bare metal. Both should be infinite ohms.
My thinking here is that the element has grounded in such a way that only part of it is heating up and that this part is close to the overheating connector causing your problem.

Next would be a bad connection at the connector.
A bad connection is actually a resistance. When electricity passes through the connection it causes heat and could give you the problem that you have.
Check that the heater connector and the wire connector are clean and properly crimped. Check that the wire connector is tight on the heater connector.
Measure from the heater connector to the other end of the wire that connects to this connection. Use the most sensitive scale on your meter.
Short the meter leads together before taking the reading so that you can see if the meter has a zero offset.
The measurement should be 0 ohms.

I hope the above helps!!