If you have a DMM (Digital MultiMeter) or access to one, you could use its' Ohmmeter function and do some static tests (tests without power connected) which may give a clue as to what is going on.
Also is the circuit breaker that keeps tripping a current protection switch or safety switch (I don't know what they are called where you are, I know them as an RCD (residual current device - detects current flow from active to ground) or just a normal circuit breaker?
The following tests are indicative only as I do not have access to the actual electrical circuit diagram for the Griller.
1. With the griller disconnected from the power outlet, connect the Ohmmeter's test leads across the active (line) and neutral pins of the griller's power cord plug, switch on the griller's On/Off switch and turn the temperature control to maximum. Take note of the resistance reading on the Ohmmeter.
2. Next place the Ohmmeter test leads between the active pin of the power plug and a suitable shiny metal contact point on the griller body and measure the resistance. Leave the griller power switch On and the temperature setting at maximum when you do this. Increase the Ohmmeter scale to maximum if you get no readings on the lower scales. Hopefully you will get a reading in the several Meg Ohms, if any reading at all. If not sure of which is the active and the neutral pin, do measurements from both.
Disconnect the meter from the griller and switch the griller off.
Now plug in the griller back into the power outlet and switch it on, set it to maximum temperature and wait for it to trip the breaker.
Once it has tripped the breaker, remove the power cord from the power outlet and perform the same tests as above using the Ohmmeter.
Be careful when you test between the active and the body of the griller it may be warm to hot.
My thinking on this is that either the temperature control switch circuitry might be faulty on the maximum setting OR that due to the heat there may be some sort of expansion going on in the griller which is causing something to short out to the body of the griller (which should be earthed - has it got a 3 pin power plug or only 2? - if only 2 it means that it is double insulated which could still be a problem if you have a RCD breaker.
Apologies for the long answer and hopefully it is of some help.
How old is the griller? Have read that Grundig has a 3 year warranty on their small appliances. This may not be applicable to your location. If you have had it less than this length of time you may wish to follow it up. Just a thought.