Provided that both the melting point, Tm, and the glass transition temperature, Tg, are both above room temperature, then you have a viscoeleastic solid. Generally, a viscoelastic solid responses, at room temperature, like a normal elastic solid to brief high stress rates, but it can also exhibit pronounced creep when exposed to either low stress rates or prolonged stress. In creep, the strain in the material keeps increasing as long as the stress is applied or until either the stress is removed or rupture eventually happens.
I suggest that you check the following RG discussions: https://www.researchgate.net/post/Is_it_possible_to_get_lower_glass_transition_temperature_when_increasing_heating_rate https://www.researchgate.net/post/Does_the_heat_capcity_of_second_order_transition_affect_by_heating_rate