Do you have a thermometer? Does it go to 160 degrees Fahrenheit or 71 Celsius? If so, pluck out a beef chunk and slap the thermometer in it (so the tip's in the middle) and take a reading. When that beef hits 160 degrees, it's completely safe from anything bad and also less than full of grelicious beef juice. 145 F (62 C) will do if you like your beef rare.
I'm guessing "low heat" is probably close to 200 F, so you're likely fine to leave it on. Most likely, with diced beef, you're fine if you've already sauteed it and haven't let it get cold.
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My favorite chili uses only one pot and includes venison, but lamb or bacon will improve the beef flavor nicely as well. BE FOREWARNED: Venison stinks like a motherbitch when it cooks, but the beef mellows it as much as it enhances the beef. Also, if you can't get good venison from a properly-aged deer, skip it entirely. No deer past 5 years old has any business being cooked, nor any younger than 3.
Choop's Venison Chili (yields 4-6 servings)
1lb. venison, in cubes (or lamb, or 1/4 lb. bacon in a slab)
1lb. beef, ground
1 14oz. can whole peeled tomatoes in sauce (not in puree nor water, though puree's better than water if you can't find them in sauce)
1/2 6oz. can tomato paste (the thicker you like it, the more you add, up to 1 can)
1 Anaheim chili
1 Poblano chili
2/3 cup olive oil, approx.
1/2 cup onion, minced
2 cloves garlic, minced
1tbsp salt (sea salt, raw salt, kosher salt, in order of preference; less if using bacon)
1tbsp crushed black pepper
1/2 tsp cayenne
1/3 tsp cumin
1/3 tsp sage
dash cinnamon
dash oregano
dash basil
1 bay leaf
1 can black beans (optional)
Roast, peel, and dice both peppers. A butane torch works well, as does a toaster oven or gas stove burner. Remove the seeds, but leave the membrane - that contains the heat. Use only the flesh and membrane of the pepper.
Heat the oil over medium-high heat until the smoking point. Add the onions and sautee until translucent, about 2-3 minutes, then add the garlic and sautee another 1-2 minutes, until the garlic smells good but before it burns. Add the peppers, and sautee another minute.
Add the ground beef and brown. Add the diced venison or lamb and brown (if you're using bacon, leave it out until a bit later). As soon as your meat is browned, season with herbs and spices. Mix very well.
Turn the heat to medium-low and add the tomatoes (with their sauce/puree!) and tomato paste. If you're adding black beans, or bacon in place of venison or lamb, drain and add them now. Stir, and bring to a simmer, then turn the burner as low as it can go and still cook. Stir it every 5-10 minutes to keep from sticking; after 45-60 minutes your chili should be ready.
Also, sometimes I add a splash of beer to deglaze the pan before I add the tomatoes. If your liquid level seems low, or if you've overestimated your tomato paste, another splash or four of beer will help you even it out. I'd probably use red wine if that were what I drink when I cook chili. Neither will really change the flavor much, and the alcohol in beer or wine cooks out at like 120 degrees.
MAN I should totally get the Achewood cookbook.
Edit: On reread of your post, you got me thinking in a different direction. If your crock-pots wiring seems the least bit sketchy, put on some rubber gloves and unplug it and throw it away RIGHT NOW. Save the chili if and only if your crock-pot's cooking bowl is removable. Nobody needs an electrical fire. Nobody needs you to have an electrical fire. A new crock-pot is cheap in the long run.