How hot will a carbon electrode get in an electrolysis setup?
Supposing there is a powerful DC source, then quite hot, unless small enough electrode current density is managed. 

6 V is quite high voltage for electrolysis. But it is possible the source will not be able to provide the current for the voltage 6 V, unless the electrode area is small.

Consider also the graphite electrodes may get deteriorated by the released gas, releasing small carbon particles to the solution (remembering my own first electrolysis experiments with carbon electrodes from old Leclanché batteries, when I was 12).