  We study numerical methods for solving a system of quasilinear stochastic
partial differential equations known as the stochastic Landau-Lifshitz-Bloch
(LLB) equation on a bounded domain in $\mathbb R^d$ for $d=1,2$. Our main
results are estimates of the rate of convergence of the Finite Element Method
to the solutions of stochastic LLB. To overcome the lack of regularity of the
solution in the case $d=2$, we propose a Finite Element scheme for a
regularised version of the equation. We then obtain error estimates of
numerical solutions and for the solution of the regularised equation as well as
the rate of convergence of this solution to the solution of the stochastic LLB
equation. As a consequence, the convergence in probability of the approximate
solutions to the solution of the stochastic LLB equation is derived. To the
best of our knowledge this is the first result on error estimates for a system
of stochastic quasilinear partial differential equations. A stronger result is
obtained in the case $d=1$ due to a new regularity result for the LLB equation
which allows us to avoid regularisation.
