Acceptable fermentation temperature range.

I don’t have any specific values to suggest but a couple of considerations:

Thermal mass

A batch of beer (e.g., 5 gallons) has a lot of thermal mass which means that it will stay close to a set temperature even with wider ambient temperature swings. For example, if a fermenter is in an environment where the temperature swings 10 degrees over a time period (e.g., a day) the liquid in the fermentor will not swing that wide. Given this aspect of thermal heat mass it could be argued that a tight window of temperature is not a requirement.

Duty cycle

If you set your temperature controller to a tight window (e.g., 68 ± 1 degrees) it will turn on/off more frequently vs. if you choose a wider window (e.g., 68 ± 3 degrees). But due to the thermal mass, in a likelihood you would achieve similar results (fermenter maintained at 68 degrees). I would suspect that there are no operational implications of having a more frequent duty cycle for the heating unit so selecting a tighter window should be OK here.

Cheers!

 

First, manufacturers usually list a range of temperatures for a given strain, but it needs to be said that every strain can also operate above and below that range. The target should depend on what you're trying to accomplish. For example, lower temperatures tend to produce less esters and highr temperatures tend to produce more.

If by range you mean "how much should I allow it to fluctuate around the target?", plus or minus a degree is tight enough for me. And you won't be able to get it tighter than that anyway.

How you set your controller will depend on what settings are available, which depends on what controller you have. What model is it?

 

With an Inkbird, I thing you have a Setpoint and a Differential. The controller will give you power (to your heat wrap) when the measured temperature falls to (or below) the Setpoint minus the Differential, and will switch off again when the measured temperature is greater than or equal to the Setpoint.

So, if you want your wort temp to be 68F, want it to be tight, and want any deviation to that to be on the cool side, set your Setpoint to 68 and differential to 1. OTOH, if you want your wort temp to be 68F, and still tight, but want any deviation to that to be on the warm side, set your Setpoint to 69 and differential to 1.

 

The temperature probe is measuring the air temperature. The yeast is working inside a liquid environment. Air temp will fluctuate much faster than liquid temp. If you can get the target temp to where you want it, the wort will usually stay fairly steady so long as the cooling unit is reliable.

For both heating and cooling, keep an eye on the temperature at first. When the compressor shuts off (cooling) or the coil turns off (heat) their is still some cold or heat available. This is especially true if you are using a freezer unit.

Cheers