Sour mashing is a fool's errand. I would never do it that way. If you have a keg, you are far better off by running off your hot wort from the tun into the keg. When its down to the proper temperature, pitch your lacto. I've found that wrapping my heating pad around the keg does keep the temp in the preferred 100F range. You don't have to worry about CO2 production since lacto generally doesn't make much, so you can put the keg lid on and close it. Burp the blow-off valve every day, if you are worried.
Remember, lacto is easy to kill with typical sanitizers, so when you pour out the soured wort, you can easily knock out any infection risk.