Theoretically, If we look at the way the heat sinks in our computers work, the power draw on projectile weapons would likely only cover the autoloaders and gimbal/turret systems. Thermal energy in modern day electronics is passes through high thermal conductivity "heat pipes" made of copper to be dispersed by the aluminum heat sink fins to disperse into the air via fans/watercooling.
The same principal likely applies in the cooling of the weapons, but at the same time one has to acknowledge that "Space," lacking any form of conductive atmosphere is a vacuum with virtually zero thermal conductivity. We also have "absolute zero."
When things get too cold, they get very brittle. Firing a weapon that produces excessive amounts of kinetic and thermal energy would significantly increase the stress presented to various physical systems leading them to shatter. This leads me to believe that the energy cost can be explained by the weapons needing to heat up significantly prior to use to reduce this stress on the system.
Overall though... I can understand the OP's point. The weapons as they are are vastly underpowered compared to the resources required.
And as far as my above rant goes, bear in mind that that is all theory. Parts of what I say may be right, others may be wrong. It is however, a potential in-game explanation for things being the way they are in ED.
*edits because the autocorrect on my phone is phenomenally stupid.*