why would my temp run up on an all-night cook

@stevesails:  Not sure if you are kidding or not.

But it is true.  Cooking in a wet environment (braising, boiling, etc.) doesn't add moisture to the meat.

It's counter intuitive, and boy it really seems like it would ad moisture, but if you have any doubts, just boil some fish or chicken until it is 180 or more internal.  It will be dry when you cut into it.

What cooking in a wet environment does do is slow the cook down.  You won't be cooking higher than 212 if you are boiling chicken.  And even though the water transfers heat much faster than air (which means it cooks faster in 212 degree water than it does in 212 degree air), it is still a relatively slow cook.  This is a gentler cook, and allows you much more control and much more time to catch the food in the proper window of internal temperature. 

Which means that you are preserving moisture in the meat, but not adding it.

But since moisture isn't added, you can still damage the meat to the point of dryness by overcooking.

So, the heat sink provided by a large water pan will help moderate the cooking environment.  But the water vapor doesn't get absorbed into the meat, making it more moist.

Anyone who has boiled a lobster or crab and found the tips of the claws dried out will understand that cooking water doesn't penetrate into the meat and add (or even rehydrate) the meat to the extent we are generally led to believe that it does.

Again, Harold McGee is a great source for explaining what is really going on when meat is being cooked.  Always a good read.

on braising: "McGee goes further, asserting that the primary tenderizer is not trapped steam or localized high pressure but rather sustained low temperature, ideally below the boiling point. When the internal meat temperature registers between 160 and 180 degrees, the collagen in tough connective tissue starts to dissolve into soft, unctuous gelatin, and the meat fibers, once bonded tightly together by the connective tissue, become easier to separate and, thus, more tender. To keep the internal meat temperature in the ideal collagen-melting range, McGee recommends setting the oven to between 200 and 250 degrees and keeping the pot lid slightly ajar. At an oven temperature as high as that which Kamman suggests, the outer portions of the meat will “overcook badly,” he contends."  (rather than thumbing through "On Food and Cooking", I found this quickly HERE)

He does say that allowing the meat to cool in the cooking liquid will allow it to reabsord some lost moisture, but this does not occur during the cook.  And not at all what a water pan would achieve.

To cook meat, in any manner, is to do cell damage.  This releases water on a cellular (i.e. micro)  level. After that, the meat is a sponge (i.e. macro level), and it is shrinking during cooking (or force during cutting while serving/eating) which squeezes water out. The only way to get water into the cells is to brine it, and let the salt do the work. But once out, the dry meat stays dry.  Even storing overcooked meat in water (like, when adding burnt tips to a stew or chili) means nothing more than meat which is wet on the outside and dry on the inside.

Cooking in a moist environment slows the cook, permits better control, less chance to dry out (because you have more time to properly take temperatures, and the thermal inertia is lower, less overrun).  You may end up with more moist meat, but it isn't because it is added moisture.  And you can still cook the meat utterly dry in such an environment.