I don't think a spectrograph would work. Solids and liquids, unlike plasma, emit black-body radiation, as far as I know. What's more, the materials in question are very likely to be a witches brew of everything from metals, other inorganics, burnt plastics, and whatever else was in the fire.
The truthers do try to claim that they can determine temperature - and even composition - from photographs. Problem there is even worse: you don't know what the original camera's colour fidelity was like, not to mention what's been done to the picture afterwords (e.g. JPEG compression) - and then viewing it on an uncalibrated monitor. Composition is right out, too (one of the regulars at ISF posts a picture of fire cinders falling off a cliff - it looks like molten metal due to exposure and colour reproduction).