Hello there
I had the same issue with one of my KZ1300 1981, it was as stupid as the throttle cable being compressed under the tank not fully releasing the detent once the bike was warm, Took the tank off the bike and re routed the throttle cable in the right passage way and that was it.
I cannot guaranty that it will be same for you but its worn fiddling around with the throttle cable, now since you have a DFI it also an issue with your mother board, I once consider buying one of the Injection Z1300 but my mechanic told me that once the mother board is acting up its better to change it and its costly....
I wish you good luck as those bikes can be very demanding and after going through four of them I finally gave up could not afford the expenses and time involved in figuring it out, my heart still beats for these Bitchy bikes but finally converted to a 2010 VRF/Interceptor 1200 with all the modern components, ABS brake and no mor issue at cold start and I am thrilled about it....
Good luck to you