I can't give a specific temperature, as there's issues:
- The sharpness is a chemical reaction which mix when the garlic cells are damaged.
- Cooking the garlic before damaging the cells will convert the chemicals before they've had a chance to react.
- Cooking the garlic after the chemical reaction will also remove the sharpness.
- I've never tried taking the temperature of garlic as it's cooking
Now, if you're cooking the garlic cloves ahead of time (I roast a couple of bulbs at a time, then squeeze out the cloves into small jar and keep it in the fridge). It'll take 30min to an hour, depending on what temperature you're roasting at (350-400F; I'll throw it in with something else ... not worth heating the oven just for garlic)
If cooking after you've cut it, it'll only take a quick saute as you have more surface area (maybe 1 to 2 min, depending on pan temp) -- but be careful, as overcooking garlic will burn it, which is just nasty. And don't do it in a dry pan, unless you're planning on ruining your dinner. When it's golden, you're done ... don't let it get to brown, as brown is that stage right before black and time to clean the pan before starting again.
Also, it seems counter-intuitive, but finely minced garlic is more potent than coarsely chopped garlic, as you're doing more damage to the garlic. It won't help in this particular case, but in many dishes that just want the garlic flavor without being overpowering will use more garlic, but slice it rather than mincing, saute it in olive oil, then remove the garlic pieces, and use the garlic-infused oil for the dish.
So, anyway, not not exactly answer the questions ... I'd go with low and slow cooking ... specific temperatures are going to lead to fast cooking garlic, which gets you burnt garlic and ruined dishes.
In dishes where you can, infuse the oil, then remove the garlic. And if you really have to, there's always garlic powder.