Oh dear, we've been moved down into the dusty basement that is "Non Air Transport Issues"!
Regarding the speed at which it is possible for a thought to be transmitted. Presumably this means the speed at which it is possible for one person's mental state to influence someone else’s mental state. In that case, if you confine the analysis to generally accepted routes of transmission (i.e. the recognised sensory modalities) then of course it is possible to quantify this sort of thing. A smile most certainly travels across a room at the speed of light! However, it takes a while to generate the smile in the first place and some time to transduce the signal at the other end - i.e. to perceive and be affected by the smile. These temporal lags should be quantifiable though.
But why do I get the feeling that this discussion is going to focus on methods of thought transmission that do not involve the extensively studied sensory modalities - i.e. the visual, auditory, olfactory, tactile, gustatory.
I think it’s important to make a distinction between how thoughts are known to be transmitted and interesting hypothetical ways in which they could be transmitted. I acknowledge that this latter topic is interesting in its own right even if there is no evidence that humans actually use the methods under discussion.