  The interplay between quantum and thermal fluctuations can induce rich
phenomena at finite temperatures in strongly correlated fermion systems. Here
we report a {\it numerically exact} auxiliary-field quantum Monte Carlo (AFQMC)
study for the finite-temperature properties of three-dimensional repulsive
Hubbard model at half filling. We concentrate on the complete
temperature-interaction strength phase diagram of the model, which contains the
low-temperature antiferromagnetic (AFM) long-range ordered phase and
metal-insulator crossover (MIC) in the paramagnetic phase. Enabling access to
unprecedented system sizes up to $20^3$, we achieve highly accurate results of
the N\'{e}el transition temperature for representative values of on-site
interaction $U$ via finite-size analysis of AFM structure factor. To
quantitatively characterize the MIC above the N\'{e}el transition, we have
developed fully new techniques allowing to compute the thermal entropy versus
$U$ at fixed temperature and to directly calculate the $U$-derivative of double
occupancy in AFQMC simulations. Then combining variously thermodynamic and
dynamical observables, we establish an efficient scheme to precisely determine
the boundaries for the MIC by cross-checking different observables. We also
demonstrate the temperature dependence of many commonly used observables. Away
from half filling, we explore the behavior of the sign problem and AFM spin
correlation versus hole doping, and demonstrate the persistance of N\'{e}el AFM
ordered phase to finite doping with limited results.
