  The Landau--Lifshitz--Bloch equation (LLBE) describes the evolution of
magnetic spin field in a ferromagnet at high temperatures. We consider a
viscous (pseudo-parabolic) regularisation of the LLBE for temperatures higher
than the Curie temperature, which we call the $\epsilon$-LLBE. Variants of the
$\epsilon$-LLBE are applicable to model pattern formation, phase transition,
and heat conduction for non-simple materials, among other things. In this
paper, we show well-posedness of the $\epsilon$-LLBE and the convergence of the
solution $\boldsymbol{u}^\epsilon$ of the regularised equation to the solution
$\boldsymbol{u}$ of the LLBE as $\epsilon\to 0^+$. As a by-product of our
analysis, we show the existence and uniqueness of regular solution to the LLBE
for temperatures higher than the Curie temperature. Furthermore, we propose a
linear fully discrete conforming finite element scheme to approximate the
solution of the $\epsilon$-LLBE. Error analysis is performed to show
unconditional stability and optimal uniform-in-time convergence rate for the
schemes. Several numerical simulations corroborate our theoretical results.
