360 running on 4 cylinders

Things like gas tank, timing, fuel filters, etc. are not going to effect just those 4 cylinders. It would also be extremely rare for the spark plugs on those 4 cylinders to not have a problem cold, but, to have one when up to operating temp. Same goes for valve adjustment on a hydraulic system. As has been mentioned, you need fuel, spark, and compression (along with the correct timing and fuel/air mixture!) so, this is something specific to these 4 cylinders that changes as the engine gets hot. Either these 4 are not getting fuel or the right mix, not getting spark, or losing compression for some weird reason.