  We address a question concerning the issue of existence to a Boussinesq type
system with a heat source. The problem is studied in the whole two dimensional
plane and the heat source is a measure transported by the flow. For arbitrary
initial data, we prove global in time existence of unique regular solutions.
Measure being a heat source limits regularity of constructing solutions and
make us work in a non-standard framework of inhomogeneous Besov spaces of the
$L^\infty(0,T;B^s_{p,\infty})$-type. Application of the Lagrangian coordinates
yields uniqueness omitting difficulties with comparison of measures.
