Thanx for explaining this: It is no build for me, as it is too complicated for me to use extra stuff during combat, but it is interesting to know this can be done
Full silent running (SR) builds use the hull tank ie HRPs & MRPs with predominantly heatsinks in your utilities, but they are only really useful for PvP because NPCs have the uncanny ability to ignore the SR mechanics and are able to sense your presence/hit you even with very low heat signatures. NPCs ability to target your modules using powerful weapons like rails with unerring accuracy is also an issue here.
Two main ships for SR are the DBS & FAS - I have both for PvP but if your opponent has emissive weapons (which heat up the target) these battles have to become highly strategic affairs - if you want to win, that is - where you have to break off the attacks to cool down again; 'still viable, but you will need patience because fights can last 20+ mins & personally I lose the will to live (in game - literally) after about 10, with ~5mins my preferred duration sweet spot!
This is a far cry from the halcyon days of SR when one could fly around in 'invisible mode' spamming heatsinks & fighting as usual keeping heat signature down even when firing weapons in SR.