| Only plemum rated cable or wiring method can be installed in a duct.
Seems you already did try the logical action by balancing the air duct system to force more air to the warm area.
THere may be a more difficult situation here, with improper insulation causing the second floor to loose what cooled air is delivered and the outside heat is not being kept out, and the cooled air cannot overcome and maintain temperature.
Try running some cable temporarily to the second floor along with the stat for a few days to see if your plan will help, however, I do belive you are correct in that the unit will continue to run longer to attempt to maintain temp. really should look at the insulation situation because all your cooling will be wasted. |