Calculating electromagnet – magnetism vs heat
Just working through your example, a coil diameter of 10mm, wire thickness of 0.8128mm, means ~32.7mm per turn of wire length, so for 500 turns you have 16,350mm of wire length, 

for that length and wire size, you end up with 0.55 Ohm for the entire length, of which the heat has to be spread over the surface area of your coil based on how many turns and how thick the wire is, from a quick cross check I am going to have to assume you where planning multiple layers for the coil (a single layer would be 40cm long), which will increase the total length, resistance, and drastically reduce how much surface area you have to dissipate that heat, 

Now for how hot things will get, specific numbers get difficult without simulation, instead I would focus on what you can do to reduce the power for the same magnetism, or the other way, increase magnetism for the same dissipation

For single layer coils, doubling the coil diameter increases the length of each turn by double, and doubles the surface area, so you do not actually see any significant cooling providing you have the same amount of current flowing each time, in other words the coil diameter is mostly irrelevant, 

Every time you increase the wires diameter by 1.414 times, it decreases the wires resistance by 2, but also increases the total length slightly, and increases the surface area of the coil by about the same amount. so for the same current, you end up with ~50% the original dissipation, and slightly more surface area to dissipate it over, this is all well and good, as long as it is a single layer, 

When you stack multiple layers on top of one another, well lets say you just decided to increase the thickness of your wire by 1.414 and want to keep it the same length, so you make this coil 2 layers thick and add ~40% more turns to make up the same power dissipation of the original coil, the second layer has a wider diameter, so it is longer per turn, but unless your coil diameter for the first layer was about the same as the wire thickness, it will generally be only a fractional increase in diameter, leaving you with about the same total power dissipated with a slightly increased surface area from the larger diameter of the extra layer, and ~40% more magnetism

From this you can iterate the math forward to work out your relative power dissipation for different wire thicknesses, layer counts and coil diameters, in general thicker wire reduces the total dissipation, a larger coil diameter increases surface area, and layer count is a trade off between total dissipation and surface area,