It would seem that Planck's law implies that objects of similar radiation spectra have the same temperature if the objects are "similarly close" to being black bodies.
Am I right to infer that burning red coals and red-hot iron have approximately the same temperature (which?) because they are both emitting mostly red light?
You're pretty much right and the principle - that many hot bodies are "nearly" black bodies and therefore the colour of their radiation is related to their temperature through the Planck law (or, more succinctly, the Wien displacement law) - is the basis for the optical pyrometer (see this page on howstuffworks.com). There are some approximations though. Hot surfaces are always at least slightly differenty from true black bodies and this difference is summarised in the emissivity (see the wiki page with this name) which is a scale factor defining the ratio of light emitted from a hot surface to that emitted by an ideal black body at that temperature. The complicated physics giving rise to a nonunity emissivity can be frequency dependent; if so the spectrum will be distorted and an optical pyrometer, as well as we, can be tricked into thinking the temperature is different from what the body's temperature really is. However, your principle is a good one, especially as a rule of thumb and your physical reasoning is very sound and admirable.
