Williams wall heater shuts off
The idea that one part is espanding and contracting whil another is not, and then slips under screwheads seems reasonable. Loosen the screws and allow it to go through a heat up and cool down cycle. I the noises are gone, then that was the problem, if not, then look somewhere else. Mind you, this should be a temporary action, not a solution, retighten when finished with experiment.
If you discover that to be the problem, then there may be a solution, though not an ideal one. Since what is happening is that one item is expanding while another is not, this means that there is a temperature differential between the items. If you can reduce or eliminate the differential, the problem might go away. I suspect that one item heats, and the other does also. Perhaps, if you turned the gas petcock partially off (in the bottom of the unit - follow the line from the control to the supply) you would effectively lower the BTU of the burner assembly. If you do this, be sure to observe the color of the flames in the burner - if they remain the nice blue as described in the manual, but are just a bit shorter, you should be o.k. If the flames go yellow, abandon this idea.
In this way, the heater will not heat up the rapidly expanding part so fast, and the other part might get some time to catch up. Of course, the room wil not heat up as quickly, but most likely it will still reach the desired temperature. The cycling of the control (if thermostaticaly controlled) will be reduced and it an the burner and heat box will have a longer life.
Now the disclaimer> I have worked in the HVAC field, and I have done this on my own Williams wall unit, and it worked. Never-the-less, I do not claim to have suficient expertise to evaluate this method as sound or safe, so you should consult someone more qualified than I, and assume all risks for your own actions, as well as not attempting anything that you do not understand. Good luck.