Is it possible to improve electrolysis rate without increasing heat? I'm separating water into hydrogen and oxygen by connecting a DC current to 99.9% pure nickel electrodes in a solution of NaOH in deionized water.

It works great, except that any attempts to increase the rate of production by increasing current, increasing NaOH, bringing electrodes closer together, etc. also result in an increase in heat.

At the moment the bottleneck for my production rate is trying to keep the water from boiling or otherwise causing heat damage to the apparatus.

I've considered investing in a cooling system, but I'm also interested in knowing whether or not it is possible to somehow improve the efficiency of the electrolysis and thereby improve separation rate without increasing heat.

(In case you're wondering, I'm using hydrogen to fill balloons.  It works quite well, I can fill a normal sized balloon in a few minutes, but then I need to wait an hour for everything to cool down.  (Yes I know hydrogen and fire don't mix well.))
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!