We　study　the　Cauchy　problem　for　the　2D　incompressible　MHD-Boussinesq　equations　without　thermal　diffusion.　We　prove　the　global　existence　and　uniqueness　of　the　solutions　for　suitably　regular　initial　data.　To　obtain　large　time　decay　properties　of　the　solutions,　we　insert　an　artificial　thermal　damping　term.　By　applying　the　classical　Fourier　splitting　methods,　we　derive　optimal　large　time　decay　rates　of　the　solutions　and　their　first-order　derivatives.