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Simplified I'm sure you have a certain meaning with that question.So, what do you mean by a hot/cold 'transparent' environment?Photons are photons as far as I know?But if we assume a very cold environment, a Bose/Einstein condensate?
They are the same but time passes faster in a hot environment and slower in a cold one. So looked at from the perspective of a distant observer they would appear to travel faster in a hot environment. The photons in the hot environment would complete their journey sooner than the photons in the cold environment. Both sets would have taken the same local time but a second is shorter in the hot environment.
Presumably the questioner is talking about normal solid liquid or gaseous environments and not plasma environments Which are much more opaque to photons because of the different sorts of interactionsPhotons travel slower than the vacuum speed of light in normal transparent materials and as materials usually become less dense (ie expand) a temperature rises the refractive index (a measure of the difference in the speed of light between two media usually falls i.e. the photon velocity rises as the temperature goes up but this is not always the case near to frequencies where light may be absorbed.