How to to prepare red deer haunch without using high temperature, so that its not dry?
As far as i'm concerned the secret is low temperature and patience. First of all, let's state that when cook a piece of meat as lean as red deer haunch, it is truly hard work to avoid a dry texture, given how little fat there is in your base product.

The way I handle this type of cut is to quickly sear it and then put it in an oven below boiling temperature for a LONG time. Just keep it at about 90 C and it will be good after about 5 hours (and still be good after 7)

Make sure the meat is covered in stewing liquid and there should not be any loss of moisture from evaporation. Give it that much time and the meat will become tender and moist despite missing the fat.

What I do to avoid watery flavour is to spoon some of the stewing liquid (about a liter) out into a separate pan an hour before serving and reducing it all the way down. You can then work it up to a sauce to have a creamy texture tasting like a concentrated versionof the stewing liquid. This will work regardless of the what you put in the stewing liquid, and does not require alcohol or sugar to produce a flavorsome sauce.