Hockhurz jump mash is really designed for hot water infusion, where near boiling water is introduced (usually underlet while stirring like buggery) to get the step up in a matter of minutes.
Really works best in a 2+V system. Baumeister and other 1V systems really don't get there fast enough. About 1oC/minute is as fast as you can get heat across a stainless surface without having the surfaces so hot (surface of elements included) that they are denaturing the enzymes close to the surfaces. Same applies to commercial systems with steam jacket heating on the floor and sided 1oC/m is about the limit even with the rakes going flat out.
The calculations for how much how hot water to add aren't all that complicated.
To check the temperature on a Braumeister I use a precision thermometer (0.1oC), put some water (say about 1/4-1/3 of nominal volume, run the heating and the pump in manual mode at about 65-70oC, give it time to stabilise, then take the reading. Partly because my precision thermometer goes from 40-70oC
The pump on the BM shuts down well under 100oC so just make sure you are testing while the pump is running so the water temperature is homogeneous.
Nice to note that the latest BM has a temperature offset/correction as part of the setup as well as a few other features that have been a long time coming, like a start at timer, can memorise a bunch programs... of very nice computer now.