Amorphous　alloys　have　been　widely　employed　in　electrical　engineering　but　there　was　no　enough　research　on　its　temperature　characteristics　and　the　hysteresis　of　air　gapped　core　model.　The　amorphous　alloys　hysteresis　model　including　thermal　effects　was　proposed　by　incorporating　the　temperature　into　the　original　J-A　model.　The　influence　of　thermal　expansion　effect　and　magnetostrictive　effect　on　magnetic　core　with　air　gap　was　analyzed.　The　formulae　of　magnetostriction　coefficient　and　thermal　expand　coefficient　were　proposed　to　correct　the　length　of　air　gap.　Finally,　the　amorphous　alloys　hysteresis　model　including　thermal　effects　and　air　gap　factors　was　proposed.　A　new　design　of　air　gapped　amorphous　core　with　stable　temperature　characteristics　was　proposed　based　on　the　new　model.　The　experiments　on　a　Fe-Ni-based　amorphous　core　were　conducted.　The　results　show　good　agreement　between　the　simulation　and　the　experiment.