You have to have somewhat of a deadband to prevent short cycling the compressor. I do industrial controls and were I to design a system like this, I'd think that 3 degrees or so would be appropriate for the application. The constant starting and stopping of the compressor would be harder on everything with a deadband of +/- 1 degree than it would +/- 1.5 degrees which is essentially coming on at 39 and shutting off at 37 to maintain 38. The beer temperature isn't going to swing quite like the air temperature does.
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