I know that heat destroys perm magnets, but how about electromagnetics? Does heat affect the strength of an electromagnetic field?
No, heat has no influence on the strength of a magnetic field produced by current flowing around a coil of wire. The strength of that magnetic field is strictly the result of the ampere-turns of current going around.
However, heat can effect the magnetic permeability of various materials. If the electromagnet has anything other than a air core, then how the field resulting from the ampere-turns is concentrated and shaped can differ with temperature. This concentration and channeling of the magnetic field can make a electromagnet appear to have a stronger field, and can make it act "stronger" in many applications.
For example, let's say you wrap 100 turns of wire around a wooden rod and put 1 A thru it. The magnetic field strength is strictly a function of the 100 ampere-turns of current going around. However, this magnet will be able to pick up heavier objects if the wooden rod is replaced by a iron rod of the same shape and size. This is because the iron is a much better conductor of magnetism than air and wood are, so the magnetic field lines will be concentrated at the ends of the iron rod. This more concentrated field is able to pick up heavier magnetic objects as a result of this concentration, even though the overall magnetic field has the same average strength in both cases.
In the example above, the apparent strength of the electromagnet with a iron core depends on material properties of the iron, which can vary with temperature. The magnetic permeability of free space is not effected by temperature, so the same coil without a core would make a magnet that does not vary with temperature.
Of course extreme tempertures change the wire and will eventually melt it so that you don't have a electromagnet anymore at all. That obviously changes things, but I'm assuming that's not the kind of effect you are asking about.
Since the MMF power of an electromagnet is a function of currnet (A*t), and current can limited by resistance and resistanse is higly depented by the temperature, so YES when temperature in electromagnet increase (due to wrong design), MMF will decrease accordingly. Try to wind randomly a wire to a random form. Appling a random DC power and voi la.. two main possibilities: One is the electromanet to have a very weak force and almost not responds. The other is to see an attraction of a piece of metal, but after a some minutes the coil becomes very hot and metal releasd.
You have to be careful about what you mean by magnetic field. It is a term that is used for two closely related terms the H - field and the B - field. The B-field is known as the magnetic field and also know as the magnetic flux density is measured in units of T (Tesla). The other magnetic field also know as magnetic field strength and is measured in Wb (Webers).
These two fields are related to each other via: $$ B = \mu H + M $$ Where M is the magnetization, for para- and dia- magnetic material this becomes simply: $$ B = \mu H$$
With \$\mu\$ being a material constant that may or may not be affected by temperature. A case in point is the Curie temperature of certain materials that when exceeded the material looses it's magnetic properties.
If you use H as your "magnetic field" then it will not be temperature dependant because H is material independent.
This confusion is due to sloppy usage or people not realizing the difference.
The most common usage is to call the B field the "magnetic field", it's not uncommon to hear people use units of Tesla or Gauss (both are units of flux density).
If only the field is subjected to reasonable changes in temperature, the answer is "No."
However, since electromagnets have to be wound with something conductive in order to generate the desired magnetic field, and since the resistivity of all elemental metals increases as temperature increases, the resistance of what the coil is wound with (copper, usually) will increase as it gets hotter.
That means that with a fixed number of turns and a fixed voltage driving the coil, as its [the coil's] temperature increases, the current through it will decrease, weakening the strength of the magnetic field because of the coil's diminishing ampere-turn product.