For a coiled wire to act as a transformer, the coiled wire would need to be placed in such a way as to have it's magnetic field interact with another conductor.
That said, you will get Inductive reactance around a coil of wire, which is measured in Ohms same as resistance, and can and will generate heat. This won't be the case with a coiled power cord however as inductive reactance is a product of the magnetic field a coil generates. In the case of a power cord the magnetic fields from the power and return wires cancel out. A tight coil might have a little more difficulty dissipating heat due to lack of airflow but you won't be getting any additional inductive reactance heating. It's somewhat common in aircraft wiring to run power and ground wires in twisted pairs to cancel out magnetic fields which can be troublesome in many ways.
