The TX Valve as mentioned in the image posted above this post has an acorn nut on the left side as you look at it. Remove that nut and there is a slotted screw for super-heat adjustment inside. In short it modulates the opening & closing of the TX valve relative to the sensing bulb when the unit is running.
Ideally to maximize efficiency, the TX valve needs to be closing down right at the threshold of your low pressure cutout. With the system running from relatively warm, the valve will be open further and you'll often hear the TX valve hissing this gradually drops off as the holding plate cools down.
You can adjust the super-heat to balance the system - never adjust more than a quarter turn. Without gauges its difficult, however frosting on the suction side return can be used as a guideline when the unit is at its coldest. Use the low pressure switch setting as the fixed known pressure point - (more on that further down)
You do not want the frosting to reach close to the compressor - TX open too much. Likewise the outlet of the plate should be frosted if its not, the the TX valve is probably closing too soon. All of this needs to be done at the end of the cycle. Thermostatic controls will often cut the compressor too soon so set it to max or the equivalent of always on for adjustment purposes. Additional factors are the distance between the outlet of the plate how much of the return is insulated and if you have a receiver in the system or not.
Back to that low pressure switch - most, you can see the set point - for your system -20C is 6.38PSI on the return vapor line - I'd set the LP switch to 5PSI which will be about -21C.
Keep the compressor running by maxing the thermostat. Let the system pull down to as cold as you think it will currently go, afterwards adjust the super-heat gradually 1/4 turn at a time and waiting (always with compressor running) 5-15 minutes. If you close it down too much the pressure will drop and the LP switch will shut off the compressor too early, if open too much icing will form too close to the compressor putting it at risk of damage from liquid refrigerant and the pressure will not drop. Its a balancing act between amount of icing on the return and super-heat adjustment. Not for the faint hearted but doable without gauges if careful & making slow incremental adjustments.
If you can determine whether there is a receiver in the system or not, that would help - its better to have one, you can use it as your frost reference point - adjust super-heat until frosting has reached the inlet of the receiver only, no further. The receiver is used to pump
the system down and as a large expansion tank to prevent liquid refrigerant reaching the compressor - basically a large can allowing any liquid slugs to boil off in the largish open space and last component on the return side before the compressor.
A couple of pics of the compressor and associated pipework close by would help me show you where I would find acceptable as my frost cutoff point if you can't find a receiver in the system.
In summary, r437a should be quite capable of pulling a hold over plate system down to -20C and needs to be set up accordingly. See the pressure chart linked below.