Hope I'm recalling this correctly fr/a senior level Food & Diary Microbiology class I took over 30yrs ago. [Made quite a bit of yogurt then. Used a Salton yogurt maker for yrs to make yogurt at home.]
Ideal yogurt making temp for Lactobacillus bulgaricus and L. acidophilis is ~108 deg F (non-pathogens generally have a broader temp range for prospering than do pathogenic bacteria - hence the ability to tolerate such a high temp and do well). FYI, figure, nominally speaking, one bacterial cell division of each of the initial culture organisms in ~20min at these temps (let's see... 3div per hour, so in ~6.5hrs we have ~20divisons, so each cell will have multiplied to ~1million cells - 2 raised to the 20th power = ~1million - prolific, to say the least), I'm not sure of the actual division (mitotic division of the cell) rate at these temps. This time is prob. in the "ballpark" though. [Note: if this were egg salad, chicken or "mayo", etc., & Staph. aureus or Salmonella were doing the multiplying - one would get plenty ill - experienced this once, i.e., Staph food intoxication (often improperly called "poisoning") based upon time to onset after consuming the "spoiled" food & duration of the mass simultaneous exit from both upper & lower ends (i'm sure you get the picture) - & this from a restaurant buffet no less - take it from me, you don't want to experience this!!!].
One can make very good yogurt, in the old days of gas ovens with pilots constantly burning, by placing the cultured milk in the kitchen oven & shutting the door. DON'T turn on the gas. The heat from the pilot in the insulated oven raises the ambient oven temp enough to make fine yogurt.
You can, as you found out through your own experimentation, culture at lower temps, but it 1) takes longer, 2) runs the risk of other "buggers" (var. Streptococci [non-pathogenic ]species, for instance - i forget the others, sorry - it's been too long) taking over and outperforming the "culture" organisms, [take it from me you don't want Strep. fecalis culturing your milk - note the "fecal" in fecalis. i tasted it once as part of a "learning" experience, the Prof. said!!!], 3) the extended length of time also allows more of a possibility for mold growth. Now, I don't know if it's possible to successfully culture yogurt in the mid-80's (degrees, NOT the decade of the 1900's). Generally speaking, figure 5-7 unrefrigerated days for mold growth. Non-Lactobacilli bacterial spoilage in a day if the Lactobacilli culture organisms do not compete as well for available nutrients. I'm not sure how "lo_you_can_go" and still be successful. Never tried myself, but it should be an interesting experiment for anyone who wishes to find out (please let me know - if you try it). You might consider adding a larger quantity of "starter" if you are going to culture the entire time at a lower temp. This could give the Lactobacilli the greater numbers that they will require to become the predominant organism. Use pasteurized milk to do this lower temp culturing to make sure that the Lactobacilli do well and succeed in actually being the culturing organism just in case you use too little starter. If anyone has any experience using "raw" milk to culture yogurt, at any temp, please share this info with us. Many thanks.
In the middle east countries, Acidophilis milk is produced by filling a goat skin with goat or camel's milk, adding a "starter" culture of L. acidophilis, and hanging it in the sun. I forget how long it takes to culture it like this, but the desert is generally pretty hot - especially if it is a dark "skin"/bag hanging in the sun. When you're not on the move, you could place your cultured milk in the sun to heat it up a bit. Don't use any clear containers though, as enough UV light from the sun can penetrate both glass and plastic and kill off the little buggers. (i've seen this over and over in microbiology labs when petri dishes are left in front of a window) Anyone need proof??? After all, this IS the principle behind SODIS - solar disinfection of water - takes ~6hrs or so on a clear day - if memory serves. [Note: it is for this reason, my own personal experience many times over, that I do NOT look at my water bottle if i'm using a UV-C generating product to sterilize my water. The mfr's say it's 'ok', but i feel differently. After all if UV can get in, why can't it get out? If I'm wrong on this last point, please reply and explain why.]
As far as keeping the culture going, once the Lactobacilli dominate & lower the ph to ~4.5 to 4.0 (hope my memory is correct here - so take these pH numbers with a "grain of salt"), other buggers shouldn't be able to grow well. I'm not sure, any longer, of any "bug" that converts Lactic acid into some type of alcohol or other metabolic by product, so I don't know/can't remember what would grow in it after culturing - other than molds. maybe i can't remember b/c nothing will grow besides the mold??? Other bugs can grow in a low pH media, but these bugs,e.g. Acetobacters & Citrobacters, need other "media" for growth, wine & citrus fruits/juice - not milk/diary products). I think that you'll be 'ok' until the molds start to grow.
Sorry, I'm beginning to ramble. 'nuff said.
Hope this info helps some.