  It is proved that the category of simplicial complete bornological spaces
over $\mathbb R$ carries a combinatorial monoidal model structure satisfying
the monoid axiom. For any commutative monoid in this category the category of
modules is also a monoidal model category with all cofibrant objects being
flat. In particular, weak equivalences between these monoids induce Quillen
equivalences between the corresponding categories of modules. On the other
hand, it is also proved that the functor of pre-compact bornology applied to
simplicial $C^\infty$-rings preserves and reflects weak equivalences, thus
assigning stable model categories of modules to simplicial $C^\infty$-rings.
