According to the manual for the Spectra module on the Hitec website, the unit draws 180 +/- 20 mA. This is considerably higher than most Tx modules and could explain why it runs warmer. As for the short battery life it is a likely contributor, but amounts to less than a third of the capacity of a 600 mA pack in one hour. Cycle your Tx battery to make sure that it is charging completely. Make sure you run the Tx with at least the first segment of the antenna raised.

Ross