I went to do the bulk ferment on my cranberry walnut sourdough last night and because the house was a bit cooler than normal I decided to give the temps a little boost by turning on the oven for a bit (usually 3-5 minutes before turning it off) so that the right rear burner will then be nice and warm for a while. Well then I got distracted by a movie I was watching (can't count the number of times that's led to some kind of cooking fail, lol), and at least 30 minutes must have passed before I realized what happened. I ran and yanked it off the stove, felt the bottom which was quite hot, started filling the sink with cold water and took a couple of readings with my infrared gun - the bottom was 129 °F (59 °C) while the top of the dough was about 110 °F (43 °C) and then plunged the container into the cold water for about 5 minutes. I then dumped it onto the counter, it looked fairly flat and the interior was still quite warm so I immediately started folding until the overall temp was uniform (about 112 °F/44 °C) put it in a bin and stuck it in the fridge. It doesn't look TOO bad this morning seems like there's some life, but now I'm thinking about adding in a fresh batch of starter and take it from there. SOOOO, anyone else ever managed to save a batch under similar circumstances? ;?)
Yeast starts to die above 130°F, and you didn't quite reach that so you should be fine. Essentially you just gave it a boost. Take it out of the fridge and treat it like you ordinarily would and I expect it will rise normally once it heats up to room temperature.
If it doesn't rise (and it may take awhile) then you've killed the yeast and your best bet is to start over from scratch, any effort you put into reviving a deal loaf is likely wasted time.
It's harder to tell with sourdough, because wild yeasts won't behave the same as cultivated yeast, and we also have the bacteria to consider. But using cultivated yeast as a guide, your nearly 60 °C/129 °F would slowly kill it, while at 110--112 °F (~44 °C) it won't be thriving but will survive.
I'm surprised that even after 30 minutes it had an average temp so high - you cooled the outside and then mixed, and were still at 112 °F. So quite a lot of it must have been hot enough to start slowly killing the yeast.
Still, with commercial strains, I would expect it to survive, just take longer to rise. I can't find different figures for sourdough starters, so I would draw the same conclusion. This old answer to a closely related question "Is there any potential harm to using warm water in my sourdough starter?" suggests that a varying temperature isn't ideal but cause major harm when added to the starter - and the starter is more sensitive as it has to live longer.
So I'd leave it longer, if I had time, rather than risking over-working the dough to mix in more starter. If you're in a hurry, you could fold in more starter, or you could prove some commercial yeast with warm water, mix in a little flour, and fold that in.