Pork butt roast: slicing temp vs pulling temp
It really isn't that simple.  It turns out this question is like "how long does it take to drive 100 miles?"  Well, part of the answer is dependent on how fast the car goes!

The pork will be fully cooked, and almost certainly palatable to your taste (in terms of doneness which is always well done at these temperatures), if it reaches 165 - 170 F in any case.

The key question is how long has it been at temperatures that convert collagen to gelatin?  Collagen converts to gelatin at a temperature dependent rate, faster at warmer temperatures (within limits).   It is not an instantaneous process.

The key difference between the slicable roast and the pullable roast is the relative amount of converted gelatin.  That is the 100 miles you want to go... having enough converted to be sumptuous and delicious.

Unfortunately, that is a tricky question to answer, since the conversion reaction starts (at a glacially slow pacing) as low as 140 F if you are willing to wait literally days, and proceeds relatively rapidly at 200 F, with varying speeds in between.  This is the speed of the car.

On the other hand, the internal temperature of the roast cannot really exceed the external temperature, since heat moves to the center from outside (I know, it sounds trivial, and it is).  But the key thing is, the outside is cooled by the evaporation of water (technically the term is enthalpy of vaporization is, but that sounds complicated):  it takes a relatively large amount of energy to convert liquid water at 100 C to steam at 100 C.

Because of this, every time a water molecule evaporates from the surface of the roast, it actually cools the roast compared to the instant before.   Overall, the temperature of the outside cannot climb substantially above a certain level until it is fairly dry (and your bark is formed).   This implies the center cannot get too hot until then either.

However, the entire time the surface temperature of your meat is stalled as it dries out (and more water migrates from the center, to certain extent), the inside is hot and collagen to gelatin conversion is ongoing.

Saying your roast is done at 170 F or pullable at 190 F (a common recommendation) is an over simplification of a complicated, non-linear process.  Sometimes it is better to just recognize when you reach your destination.

The final target temperature required to allow sufficient conversion time is dependent on the size of the roast, the temperature of the oven or barbecue, the rate at which the temperature rises in the specific roast, and so on.  This is very hard to predict.

Fortunately, pork butts and other cuts used for this type of cooking are remarkably forgiving.

So as much as it pains me to say this, in this case, put aside the thermometer, guestimate based on time, and learn to test your meat by poking at it (literally, the tenderness is the goal and the test) until you have enough experience to just know.

If you take the roast out early, and find some is not pullablle, you can always wrap the un-pullable part in foil (to inhibit additional moisture loss), and stick it right back in.  Or just slice that part!

Even the failures will be delicious.

See also:  


Huffington Post article on The Stall
What makes a moist steak (or roast)? (The answer is more general...)