Is it possible to improve electrolysis rate without increasing heat?
Consider the electrolysis apparatus as a resistor in series with an EMF. Ideally, the cell voltage should be just enough to overcome the EMF (potential needed to split water), but some over-voltage is inevitable to have a decent current flow. Much of the heating is due to this wasted over-voltage. Then, to increase the efficiency and reduce heating, it's necessary to reduce the series resistance.

$\ce{NaOH}$ is already highly ionized, so adding more, beyond a certain point, is not the solution (no pun intended;). Close spacing helps, but you must leave room to physically separate $\ce{H2}$ from $\ce{O2}$. The remaining variable is electrode area: make the electrodes as large as feasible. You can further increase area by using porous sintered, or at least coarsely-sanded electrodes. 

Quantum Sphere Inc. claims to produce a more active electrode from $\ce{Ni-Fe}$ particles, though they're probably a bit pricey for filling hydrogen balloons. Perhaps they offer samples?

BTW, I assume you're using a moisture trap for the gas, otherwise bubbling hot caustic electrolyte would inadvertently wind up in the balloon, reducing lift, damaging the balloon and possibly causing severe chemical burns. $\ce{NaOH}$ is called "caustic soda" for good reason!