Troubleshooting failed bake element

Question

Bake element caught on fire. Replaced it with new one. Didn't solve problem.

Wires/connectors do not appear burned. Now being advised to purchase oven sensor kit (thermostat?). Does this seem like a logical next step?

Also being advised to purchase a membrane switch (or clock) although current one appears to be working fine. Does this sound right? Seems like overkill.

Thanks.