  We construct predictions for top quark pair differential distributions at
hadron colliders that combine state-of-the-art NNLO QCD calculations with
double resummation at NNLL' accuracy of threshold logarithms arising from soft
gluon emissions and of small mass logarithms. This is the first time a resummed
calculation at full NNLO+NNLL' accuracy in QCD for a process with non-trivial
color structure has been completed at the differential level. Of main interest
to us is the stability of the M_{tt} and top-quark p_T distributions in the
boosted regime where fixed order calculations may become strongly dependent on
the choice of dynamic scales. With the help of numeric and analytic arguments
we confirm that the choice for the factorization and renormalization scales
advocated recently by some of the authors is indeed optimal. We further derive
a set of optimized kinematics-dependent scales for the matching functions which
appear in the resummed calculations. Our NNLO+NNLL' prediction for the top-pair
invariant mass is significantly less sensitive to the choice of factorization
scale than the fixed order prediction, even at NNLO. Notably, the resummed and
fixed order calculations are in nearly perfect agreement with each other in the
full M_{tt} range when the optimal dynamic scale is used. For the top-quark p_T
distribution the resummation performed here has less of an impact and instead
we find that upgrading the matching with fixed-order from NLO+NNLL' to
NNLO+NNLL' to be an important effect, a point to be kept in mind when using
NLO-based Monte Carlo event generators to calculate this distribution.
