Could not find a JQS so am using JQ1, it should be a very close match.
Here are your parts
Replacement parts for WHIRLPOOL TEDS740JQ1 | AppliancePartsPros.comSee attachment for the wiring diagram.
Your problem could be a number of things.
First I would check the heating coil to make sure it is not grounded.
Check the heating coil.
Unplug the unit and both wires to the coil.
Check it with a meter, should be around 10 to 12 ohms.
Then check from each side of the coil to the case/frame, both should be infinite ohms (open). If not the coil may have sagged or broken and is touching the case. This can cause it to run on high and the thermostats cannot regulate.
Next I would check the main thermostat's (Item 8 in Section 3) internal heater, it should be 6,000 to 8,000 ohms. It is turned on for lower heat settings, adding heat to the thermostat and therefore lowering the unit's heat output.
If both are OK then I would replace the main thermostat as that is the most likely cause (contacts welded together).
If you want to confirm this you could heat it up on a stove to see if it will open. I use my soldering gun.
If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.
There is a good STICKY at the start of this forum about it's use.