  Temperature-dependent magnetic properties of Nd$_2$Fe$_{14}$B permanent
magnets, i.e., saturation magnetization $M_\text{s}(T)$, effective magnetic
anisotropy constants $K_i^\text{eff}(T)$ ($i=1,2,3$), domain wall width
$\delta_w(T)$, and exchange stiffness constant $A_\text{e}(T)$, are calculated
by using \textit{ab-initio} informed atomistic spin model simulations. We
construct the atomistic spin model Hamiltonian for Nd$_2$Fe$_{14}$B by using
the Heisenberg exchange of Fe$-$Fe and Fe$-$Nd atomic pairs, the uniaxial
single-ion anisotropy of Fe atoms, and the crystal-field energy of Nd ions
which is approximately expanded into an energy formula featured by second,
fourth, and sixth-order phenomenological anisotropy constants. After applying a
temperature rescaling strategy, we show that the calculated Curie temperature,
spin-reorientation phenomenon, $M_\text{s}(T)$, $\delta_w(T)$, and
$K_i^\text{eff}(T)$ agree well with the experimental results. $A_\text{e}(T)$
is estimated through a general continuum description of the domain wall profile
by mapping atomistic magnetic moments to the macroscopic magnetization.
$A_\text{e}$ is found to decrease more slowly than $K_1^\text{eff}$ with
increasing temperature, and approximately scale with normalized magnetization
as $A_\text{e}(T) \sim m^{1.2}$. This work provokes a scale bridge between
\textit{ab-initio} calculations and temperature-dependent micromagnetic
simulations of Nd-Fe-B permanent magnets.
