I've done kettle souring twice this year now, with a lactobacillus starter propagated from raw grains.
The important considerations are PRE-ACIDIFICATION, NO OXYGEN, and temperature.
From what I read (see links below), T=110F, pH<=4.5, Oxygen=0 prevent any bacteria except the Lacto from growing in your starter and kettle.
You can get a super cheep pH meter on amazon for $10, and calibration fluid for another dollar or 2.
The steps are (presuming all standard cleaning/sanitation has already been done):
Starter: (more info:
https://www.fivebladesbrewing.com/lactobacillus-starter-guide/ )
1) put 2 cups raw uncrushed malt in container (beaker)
2) add starter wort (1.030ish)
3) add Lactic or phosphoric acid to bring down to pH 4.5
4) top with water (and/or CO2) to remove almost all head space)
5) use an airlock or saran wrap + rubberband to prevent oxygen exposure
6) hold at 110F for 2-3 days
7) pitch to 110F wort (boiled then cooled) through a strainer
Wort: (more info:
http://www.milkthefunk.com/wiki/Sour_Worting#Souring_in_the_Boil_Kettle )
1) make your wort as usual (I did stovetop BIAB in a stainless kettle).
2) boil it a little, to kill bacteria. DON'T hop it.
3) pitch lacto starter, stir gently
4) check pH, add more acid if needed to lower pH to 4.5
5) cover with saran wrap, purge all headspace with CO2
6) hold at 110F for 2-3 days, feel free to use a kettle valve for samples to check pH
7) when at 3.4 to 3.2 pH, depending on how tart you want it, boil it with around 5 IBU of neutral german hop (hallertauer)
-- bacteria are dead at this point --
8) proceed to pitch/ferment as for normal ale.
I've used all-brett (frutier, slower to ferment) or US-05 (fast and clean). I am told you could use both for a more traditional funk. may take a little longer than normal to ferment because of low pH.
I also dry hopped with 1oz mosaic/simcoe in a keg, and it was excellent.
To answer your actual question on holding temp, a temperature controller + fermwrap around the kettle, surrounded by a blanket or something, should work. I have the luxury of a homemade temperature chamber (insulated plywood box with fridge+heater.
For the starter, I had a fermwrap in a 5gal bucket with the 2L beaker, using my temperature controller set at 110F.