temp control advice needed

I am using the stc-1000 temp controller. I have the probe submerged in a container of water. I maintain steady beer serving temp of between 37 - 37.8 degrees. My question is about the settings on the controller. How much of a temp swing can I allow before it effects the beer? Right now I have it set at .6. I know the water will warm faster cause its a smaller volume and that's where my question is coming from. I don't want to work the fridge more then needed so if I can open that temp swing up I would like to. Thank you very much in advance for all responses. If you I left out any info needed just ask I will tell. Thanks again

I have mine set to 4.4*C (~40*F) with a differential of 3*C, so my high end kicks off at ~45*F. My probe is in a gallon of water also. I have a 4 keg setup. I think that my compressor kicks on about twice a day and runs for an hour or so at a time. I'd like to go warmer, but my wife likes the beer colder than I do, so I've compromised and set this range.

I have mine set to 2 degrees, compressor barely evern kicks on. It is in the basement, however.

2 degrees c or f? Is me having it .6 too close? The probe is only in a typical water bottle