the autotune will when set up to run in the conditions you want the pid to work in, vessel size, volume and starting temp and target temp. run through the process of heating up taking much longer than normal measuring the effect of the input given to the heating element. from this it will derive the 3 control parameters that govern how the pid opperates tuning it to your circumstance..
once auto tuned the pid will perform the job you tuned it to with the most efficient use of energy possible according to the pid algorithm. however the efficiency savings per brew will never in my opinion make up for the extra hours the thing is on performing the autotune in the first place
when its an industrial job however with huge energy costs, any saving is worthwhile..