Is there any evidence to support a correlation between how much bodily energy you are using, and how quickly time appears to pass?
There's literature on temporal expansion with vigilance.  Perhaps this might get you started.

Tse, P. U., Intriligator, J., Rivest, J., and Cavanagh, P. (2004). Attention and the subjective expansion of time. Perception &amp; Psychophysics, 66(7):1171–1189.

In this instance they're looking at how odd, unique, or surprising events might increase the amount of attention applied and that those events seem to last longer than othewise very comparable ones.  The literature reviews speaks a bit to what you've asked about.