The thermostat pilot light stays on when no function is on on a baumatic 187.12ss

I am going to say you have a faulty thermostat.

Instructions

1. Access the burners inside your oven by removing the access panel in the front of the oven or by opening the broiling drawer, depending on your particular model.
   
2. Determine if the pilot itself is lit, since some ovens have a small flame on the pilot at all times that then grows and extends to the burner when the oven is turned on. The lack of a pilot flame indicates the oven thermostat is malfunctioning or there is a problem with the gas hose. Check the pilot itself to see if it is clogged with debris or grease that could be preventing the flame from staying lit.
   
3. Determine if the pilot flame will grow if it is lit by turning on the thermostat. If the pilot flame doesn't extend, the thermostat itself likely needs replacement. If the flame is extending but the gas valve is not opening, the safety valve could be dirty or defective. The flame should be blue in color. A yellow flame indicates the pilot is dirty and is not burning hot enough to get the main burner to ignite.
   
4. Light the burner on the top of the oven with a match if the igniter doesn't appear to be effective. If it lights manually but will not light automatically, the igniter is likely faulty. Do not do this if there is a heavy smell of gas in the kitchen, since there could be a risk of a fire. In that circumstance, turn the oven off, ventilate the room and call a technician.
   
5. Listen for any sounds of gas hissing or a clicking sound indicating the oven is trying to turn on. If there is no response from the oven at all, the gas may not be functioning properly and will need to be examined by a technician for safety purposes
   

From the symptons described, I would say that the thermostat is faulty that controls the oven temperature, normal procedure is replace the faulty thermostat.

sounds like the heating element, also check the thermostat

For this to happen, indicates a faulty thermostat that controls the oven temp, I would fit a new one

Could be both parts are faulty from symptoms you describe.
The indicator light should not be on if it is in the off position, this would suggest the thermostat is faulty.
On the other hand, if the element is faulty, then obviously, there will be no heat
To be certain if the element is faulty or not, then you need to test the element with a meter.

It sounds like the thermostat is faulty, make sure the sensor is not detached inside the oven compartment, as this will affect the thermostatI if it is. If o/k, then the only option is to replace the thermostat. If it is fan assisted, then make sure the fan is working o/k as well.
Please leave a rating for my comments.
Thganks.

Disconnect the element, and run the oven for at least 30 mins,,if it does not blow fuse, then more than likely it is a faulty element.
What I cannot understand is that you say the thermostat light is on after the fues has blown? I would have thought that the light would be not be on, if the fuse has blown.
If after replacing fuse and the stat is in the off position, and the indicator light is on then indeed the stat is faulty.
Plz rate my solution.
Thanks.

Hello. Usually this problem is related to the pilot being dirty, and not heating the bulb for the safety device properly/hot enough to fully open the valve. If you have a general purpose mini torch you can heat the metal bulb near the pilot with it, if this is the problem, the safety will open, and the main burner will come on. CAREFUL, you are not on/around the main burner, as it will allow gas to come on to the main burner, and if your pilot is not working properly, might not light the gas. Get the pilot cleaned and adjusted.

or... :) I know... your safety has failed, allowing gas to the pilot, but internally is not opening, this requires replacement. Last though, it could be your thermostat, its last in line, and would require replacement. The safety, and the thermostat are mechanical valves, open or closed depending on its function.

If you have a more current type, they will have a combination valve, and thermopile/thermocouple that are electromechanical, your thermostat at this point can be either mechanical, or electromechanical. This system has a few more possible causes for your symptom.
You can tell which you have by how you light the pilot, have a red button on the front of the unit, by the on/off valve? this is the first type.
Have to open a small door to access a knob, turn it to pilot, and hold in? this is the latter type.
ask if you need more help.
Hope that helps, and thank you.