This　paper　is　concerned　with　the　initial-boundary　value　problem　to　2D　magnetohydrodynamics-Boussinesq　system　with　the　temperature-dependent　viscosity,　thermal　diffusivity　and　electrical　conductivity.　First,　we　establish　the　global　weak　solutions　under　the　minimal　initial　assumption.　Then　by　imposing　higher　regularity　assumption　on　the　initial　data,　we　obtain　the　global　strong　solution　with　uniqueness.　Moreover,　the　exponential　decay　rates　of　weak　solutions　and　strong　solution　are　obtained　respectively.　(C)　2017　Elsevier　Inc.　All　rights　reserved.