My name is Peter. I am a retired field service appliance technician.
The normal operation of a oven is the oven will rise 20-40 degrees above the set temperature and turn off. Then, when the oven temperature drops 20-40 degrees below the set temperature it will turn back on and cycle again. This is true except for the new accurate ovens.
Since you are getting heat your oven heating element is good.
You have a older oven.
Your problem is either the oven thermostat which cost over $200.00.
Or, your oven control, which base on your oven age is no longer available.
Now, here are your choices:
1.) Take a chance and purchase the oven thermostat and install it. If this does not solve the problem you can return it less shipping and restocking charges.
2.) My professional recommendation is to put the old girl to rest.
a.) Go to a Sears Outlet (Scratch and Dent) Store, save a couple of hundred dollars on a new oven and still get a one year warrantee .
b.) Go to a used appliance store.
c.) Go to Habitat Stores - used appliance stores.
d.) Go to Second Chances Stores - Appliances removed from homes that were torn down.
Best of luck,