The viscous coupling would interfere with the operation of a clutch type LSD. The correct way to run a clutch LSD in the center is to completely remove the VCU. Most of the center diff replacements don't have provisions to even install it.
Locking it with a VCE would essentially disable the LSD, turning it into a fully locked center.
Running a locked center with a viscous would also not change anything - the correct thing to do again is remove the VCU.
If you decide to run an oil cooler for the transmission, you need to be running thinner gear oil or ATF, and the cooler also needs a pump.
Quoting bazeng:
I've made about 40 dyno runs in 4th gear with 450hp - 550hp pulls without any signs of the box giving up (touch wood!!!!).
vrfour_nz, so are you running that viscous lsd and the centre lsd together?
I'm wondering why we dont lock the viscous when running a clutch type lsd?...
Or what if we ran a locked centre with a viscous?