I dont know this for certain but in terms of cooling, a standard item would obviously be ok, but not as efficient as the S3 / Ed30 coolers and so would limit what you could get from your K04 as the higher boost it can generate will need greater cooling.
Also, the pipework needed for the K04 might be different dimensions, altho as i believe you are able to relocate the DV on a K03 car using the necessary pipework then i suspect that fittings should all be fine and will just come down to cooling efficiency of the IC.
As i say, im merely guessing based on how the thing operates and am also in need of a definitive answer as i'm going from K03 to K04 as well soon.