I have been seeing this and getting this question a lot from you readers as well as on message boards and facebook groups, so i figured i would take a little time and write up an answer for anyone looking.
Thermosets are materials that undergo a chemical reaction (curing) and normally transform from a liquid to a solid. In its uncured form, the material has small, unlinked molecules (known as monomers). The addition of a second material (cross-linker, curing agent, catalyst) and the presence of heat or some other activating influences will initiate the chemical reaction (curing reaction).
The molecules cross-link and form significantly longer molecular chains and cross-link networks during this reaction, causing the material to solidify. This change is permanent and irreversible. Subsequently, exposure to high heat will cause the material to degrade, not melt. This is because these materials typically degrade at a temperature below where they would be able to meet.
Thermoplastics are melt-process-able plastics (materials that are processed with heat). When enough heat is added to bring the temperature of the plastic above its melting point, the plastic liquefies (softens enough to be processed). When the heat source is removed and the temperature of the plastic drops below its melting point, the plastic solidifies back into a glass-like solid.
This process can be repeated, with the plastic melting and solidifying as the temperature climbs above and drops below the melting temperature, respectively. However, the material can be increasingly subject to deterioration in its molten state, so there is a practical limit to the number of times that this reprocessing can occur before material properties begin to suffer. Many thermoplastic polymers are addition-type, yielding very long molecular chain lengths (very high molecular weights).
As mentioned above, thermoplastics are capable of being repeatedly softened by the application of heat and hardened by cooling and have the potential to be the most easily recycled, which has seen them most favored in recent commercial uptake. In contrast, the better realization of the fiber properties is generally achieved using thermosets.
DSC can be a good tool to determine if it melts and can re-melt thermoplastic or just Tg (example) for thermoset.
Hopefully I have answered your questions regarding thermosetting and thermoplastic polyurethane. If you have any further questions, please do not hesitate to comment below and I will be glad to answer any you might have.