The mesophilic range is 85-100 degrees F and the thermophilic range is 120-135 degrees F.

As you go pass through the mesophilic you'll probably loose your methane producers so I don't think this would work. Also changes in temperature need to be made very slowly, a degree a day or so or else you'll upset the digester.

Likely you'd have to start from scratch. Mixing is very important in these processes too, without enough mixing for a higher-rate you'll run into problems. I'd contact the manufacturer and get their take on it.

I have read a few things, so maybe I don't get the jist of the whole kit and kabootle.  I read you get better reductions and beter quality and quantity of methane.  Farms fo thermo first and then meseo last.  I really don't get that scenario.  So still my question is why not straight to thermo.......I understand if it was easy everyone would go to that range.....
I have jet mixing, I feed 24/7 by timer.  I have 4-6% feed sludge(municipal).
Reason i ask is I am into looking at composting.  What I am reading is if I can go thermo I can skip the composting operation and be class A right out of the digester to my drying bed.......Hmmmmm

Makes one think......

This was my point of asking the question, I want to try it.  But I am looking for anyone with more experience than me to give their opinion.  I am no biologist, just an operator with too much information. LOL

From a microbial perspective, the conversion of a mesophilic digester (35C) to thermophilic digester (55C) would require a more gradual increase in temperature over time to prevent upsets in microbial community in the digester particularly the methanogens.  Thermophilic digesters are more efficient but lack the stability of mesophilic digesters.  Also note, because of increased hydrolysis and methane production under thermophilic conditions, operating parameters such as retention time will need to be adjusted.