Cooking beef goulash in a slow cooker with a temperature controller, what temperature?
Here's an older answer to a similar question that is potentially quite relevant. I won't reproduce the text in full, just pull out some of the salient points.

Goulash being a stew, traditionally cooked with tougher cuts much higher in collagen, your ultimate goal is to break down that collagen into gelatin.  Traditional wisdom holds that this breakdown doesn't really begin until about 70°C/160°F, but modernist resources suggest that the actual reaction starts as low as 50°C/122°F and increases exponentially with temperature.  If you're able to maintain a sous vide style temperature using the controller, you should be able to take advantage of similar results.

From @Stefan's linked answer:


  The answer to the question, "how low can you go and still get collagen break-down" I would answer 55°C/130°F or even a bit lower. That is NOT a realistic temperature for cooking a stew, especially not if you will put veggies in it, but as far as collagen breakdown goes that is the lowest temperature for 'stewing meat'.


This also notes the challenge with cooking at such a low temperature: the vegetables won't respond to such a low temperature in the same way as the meat.  They need higher heat and more moisture to break down. You probably need to consider cooking them separately for optimal results:


  I think you must cook the veggies at much higher temperature (80°C-95°C) so you would have to separate the two. If the end result is worth the effort I do not know, I have wanted to try doing a 'stew' with meat cooked sous vide at 55°C - 60°C for 24h+, with the veggies done on the side at 80°C-95°C, normal stew style, to see if it would be better [...]


This is good guidance in my opinion; I'd let the meat go for about 24 hours to start (you could experiement with longer if you like and have the patience to do so) and quickly cook the vegetables on the stove for maybe an hour before you're ready to serve with just as much liquid as necessary.

The only thing you might miss out on with this method is the well-known phenomenon of stews tasting better the day after they're made. If you're going to experiment, consider reserving a portion of the combined result, letting it chill overnight, and then (gently) reheating the next day to see if you get the same "marriage" of flavors.