We know that if a conductor has any net charge, the charges reside on the surface. The electric field immediately outside the surface is perpendicular to the surface. But the charged particles, say the conductor has net electrons, will be in thermal vibration and increase in temperature will increase the vibrations. So, the net electrons vibrating on the surface will lead to changing electric fields outside the surface, not perpendicular all the time. Doesn't that cause a magnetic field, however small?
Yes you are right. You end up having a varying electric field which generates a varying magnetic field which in turn generates an electric field etc... This causes a particular type of radiation called black body radiation.
Yes, these thermally generated currents (Johnson noise) generate magnetic fields. This means that even non-magnetic materials generate a very-small magnetic noise if they are conductive. This actually places a limit on very-sensitive magnetic field measurements in shielded environments because the shields are usually conductive. The following Review of Scientific Instruments article (abstract) discusses this issue. Alternately, one can use high resistance materials such as ferrites for magnetic shielding as discussed in this Applied Physics Letters article (PDF).