Can heat be transfered via magnetic field in a vacuum? Say you want to store hot coffee in a container surrounded by a vacuum. To remove all sources of conductive energy loss the container is suspended in the vacuum by a magnetic field and does not have a physical connection to the sides of the vacuum chamber,
My question is would the magnetic field be a path for energy to be conducted out of the suspended container?
Another way to look at this question would be two magnets are suspended in a vacuum with their poles aligned. A heat source is attached to one of the magnets. Would the second magnet show a corresponding increase in temperature, excluding radiated heat transfer?
 A: Heat consists of random vibrations in a material. If a magnetic field connects two objects, then it creates a mechanical coupling between the two objects. Such a coupling will couple vibrations, therefore heat will be conducted by the magnetic field.
In practice, the effect will be very small, but given enough time, heat will be conducted by the magnetic field. The same applies to suspension by a combination electric and magnetic field.
This is not entirely incompatible with some of the other (wrong) answers. For example, since the suspended object is not at absolute zero, it is not possible for the magnetic field suspending it to be entirely static.

As an example, let's consider a superconducting metal container of gas suspended in a magnetic field:

Now suppose that the gas is at some non-zero temperature. Then there is a non-zero probability that the gas will concentrate onto one side:

In order for this to happen, assuming that the center of mass of the container remained constant, the metal part of the container had to have shifted in the opposite direction:

Assuming that the levitation is stable, a motion of the superconducting container must be opposed by the magnetic field. Thus the above motion is opposed by a force from the magnetic field. However, for every action there is an opposite and equal reaction (Newton's 3rd law), therefore there will be a corresponding opposing force on the suspension:

Therefore thermal motion in the suspended container will induce thermal motion in the base, hence there will be conduction of heat.
A: The various comments on the earlier Answers to this Question point to its moderately fundamental misconception. Because of special relativity there is no such thing as a magnetic field separately from the electromagnetic field. Thermal fluctuations of a body, including vibrations, are transferred to a remote body by interactions between the bodies, the chief of which is likely to be electromagnetism at scales at which magnetism has been engineered to be a specific constraint on movement.
The first part of the Question obscures matters by introducing a magnetic field without introducing its sources --permanent magnets or electromagnets, say. I think this idealization is unhelpful. If there were really a magnetic field without any source for the magnetic field, then thermodynamics would be inapplicable unless there are other heat sources; it would further have to be specified whether there are any interactions between the various heat sources, and what those interactions might be. EDIT: An electromagnetic field is dynamical, in contrast to a magnetic field, so the electromagnetic field itself can be considered to be a separate thermodynamic system, in which case the heat of the confined container will dissipate into the electromagnetic field or vice versa, depending on the relative temperatures of the electromagnetic field and of the container. 
The final sentence, "Would the second magnet show a corresponding increase in temperature, excluding radiated heat transfer?"[my emphasis] sets things up so that the answer is no by definition. If radiated heat transfer is excluded --an impossible idealization according to experience-- then there will be no change of temperature. This, however, is again not a helpful idealization.
A: No, a static magnetic field does not conduct heat.
The only way for thermal energy to cross a vacuum is by radiation. Of course, radiative heat transfer actually does consist of electric and magnetic fields: hot objects give off electromagnetic waves, which travel through the vacuum and are absorbed by, say, the walls of the vacuum chamber. But those are waves, not static fields, and besides, they are actually emitted by the hot object - it's not like it takes advantage of preexisting fields to move the energy.
A: I would say the first point to stress here is that heat by definition is the transfer of energy. 'Heat loss' can occur via convection, conduction or radiation. Clearly, the first two can be essentially reduced to zero by surrounding your coffee (or whatever) with a perfect vacuum. Creating a perfect vacuum is pretty much impossible though.
All objects at temperatures above absolute zero will radiate heat via emission of electromagnetic waves. (For more details, see this wiki article on black-body radiation.) This is a matter-of-fact, with or without a vacuum, hence why flasks don't keep your coffee warm indefinitely. A reflective layer (normally some sort of foil) is used to contain some of this radiated energy but it works better for some wavelengths, and worse for others.
To answer your question directly: no - The magnetic field used to suspend the vessel will not interfere with the energy being radiated, nor indeed does it constitute a medium through which heat can excape via any other means.
A: The magnetic field of a large magnet is a composite - i.e. an average - based upon the sum of its magnetic components such as individual iron atoms. The field can also be described as the averaged result of the point to point exchange of photons between the magnet's individual magnetic dipoles. It would be wrong to assume that the vibrations of the component point sources cannot be transmitted by their magnetic or electric charge interactions. Imagine two small magnets - say two solitary iron atoms - in close proximity with their magnetic dipoles aligned; imagine that they are held suspended in an imperfect vacuum by tiny fairies. If one of the atom/magnets acquires kinetic energy by a collision with a random gas molecule it will move and some part of its kinetic energy will transmit to its partner through the agency of their mutual electromagnetic "field". Heat has therefore been transferred by the photons of the magnetic field, in other words. That's the answer for tiny magnets. Only experiment can determine whether this same phenomenon can be manifested and to what extent at the macro scale through a magnetic field made up of the averaged and colligative behavior of large numbers of magnetic dipoles. This was actually a very interesting question.
