The present invention related to an endless belt conveying apparatus and toner image heating apparatus having spring members (thermally responsive members) composed of a shape memory alloy are disposed to both the edges of a pressure fixing belt (pressure belt) in the belt width direction thereof. When the pressure fixing belt offsets to one side in the belt width direction while it travels, one of the spring members, which is heated by the edge of the pressure belt approaching it, is deformed in response to the heat. A roller swing support frame on the belt edge side, which approaches the above spring member, is lifted upward in a gravity direction using a swing pin as a fulcrum in a gravity direction by the operation force generated by the deformation of the one spring member. The swing operation is alternately repeated between the one spring member and the other spring member to thereby correct the inclination of the pressure belt.