In a electromagnet one can basically divide the power losses into two categories, winding losses and core losses.
Winding losses are caused by the current flowing in the coil/winding of the electromagnet. These losses are equal to : P=I^2 R, where I is the current, and R is the resistance of the winding. To reduce the winding losses, the most effective method, due to the ^2 term, is to reduce the current. This again may reduce the magnetic flux density produced.
Or one can change the resistivity of the winding by changing the material (copper, aluminium etc.) or the length/number of turns of the winding. The latter also reduces the magnetic flux density.
Since the magnetic flux density is proportional to the current (I) times the number of turns(N), hence F=I*N, called the magnetomotive force (F). One way to reduce the winding losses, but still give a high magnetic flux density is to, keep in mind the P=I^2*R equation, increase the number of turns and reduce the current, keeping F constant. Thus, decreasing I but increasing R due to the increased length/number of turns. Observing that I is squared, follows that the power losses decreases.
Other losses associated are the core losses. These are related to the ferromagnetic material making the core (magnetic path of the electromagnet), if the magnet has a core.
https://en.wikipedia.org/wiki/Magnetic_core#Core_loss
The core losses are separated by the magnetic domain movement and eddy currents (induced currents) in the core. The magnetic domain movement are proportional to the changing magnetic flux density squared times the amplitude of the flux density.
Eddy currents are a consequence of a changing magnetic flux density in a conductive material. And the associated losses are proportional to the current density squared and the conductivity.
The above losses is mostly occurring using AC (alternating current) for the winding excitation, or if the material is moving in a magnetic field. Or if the external field is alternating.
An electromagnet can have both AC and DC winding excitation, that is application specific. In your case, the option is to use permanent magnets, so I would conclude that the electromagnet is powered by DC. But using DC excitation, the core losses is minimal if no movement or external field is applied. So in that case, I would say that the winding losses are the most pronounced source of heat.
