On the tensor product of two homotopy Gerstenhaber algebras we construct a Hirsch algebra structure which extends the canonical dg algebra structure. Our result applies more generally to tensor products of "level 3 Hirsch algebras" and also to the Mayer-Vietoris double complex.
Homology, Homotopy and Applications, Vol. 13 (2011), No. 2, pp.249-262.