We consider a one-dimensional thermal nonlinear medium with a step in the linear refractive index at the sample center. It is found that there exist multipole interface solitons around the interface of the sample. In this paper, we address the existences of three types of solutons for fifth-order and sixth-order interface solitons. The three types of interface solitons have diferent pofiles, beam widths, mass centers, existence and stability regions. The three types of fifth-order solitons each have a stability region, and two of them have the same regions. However for sixth-order interface solions, only one type solution has a stability region.