Most probably you are working with liquid crystalline polymer or during processing the orientation of chains are occuring partially. In the first case crystalline to isotropic transition takes place which is similar to melting. In the second case usual melting can be observed.
I think the polymer is totally amorphous; which means no crystalline phase may exist. The melting will be on a broad interval of temperatures and not a sharp endotherm. Regards
Tm is a melting temperature that crystalline polymer has it. So if your polymer is not a crystalline polymer, then it has not Tm for showing in DSC graph.
Amorphous polymers do not exhibit any peaks in DSC profiles, therefore, I think what you may have perceived as "melting" is related to the transition from rubber to liquid. Therefore, you may have seen your sample flow like a liquid beyond a certain temperature. Polymer scientists often avoid using the term "melting" for this case, to prevent confusion. Instead, they use terms like "rubbery flow" or "viscous flow" to describe liquefaction of these polymers.
For long-chain polymers increasing the temperature beyond Tg leads the material to pass through the rubbery plateau in which the material sustains a constant modulus, due to the presence of chain entanglements. Further increase in temperature leads to gradual disentanglement of the chains, meaning that the chains move fast enough to leave their confining tube. At this point (which is not very sharp for polydisperse samples) chain dynamics change from reptation to simple Rouse relaxation. In this regime the modulus of the polymer decreases to the point where the material is not able to withstand the weight of its own. Therefore, the material liquefies and loses its previous shape.