  In [2019, Space-time least-squares finite elements for parabolic equations,
arXiv:1911.01942] by F\"uhrer& Karkulik, well-posedness of a space-time
First-Order System Least-Squares formulation of the heat equation was proven.
In the present work, this result is generalized to general second order
parabolic PDEs with possibly inhomogenoeus boundary conditions, and plain
convergence of a standard adaptive finite element method driven by the
least-squares estimator is demonstrated. The proof of the latter easily extends
to a large class of least-squares formulations.
