overheating and rough idle on start
 

ok i have a mkiii 7mgte and ive been going through and upgrading things. i just put in a cx racing radiator and all new silicone hose from the radiator to the induction also i added a intake, and a hks bov. now the problem is that when i first start the car usualy after its been running and is still warm it will want to die or idle rough at about 500 to 600rpm for a few minutes and then even out. i ran a diagnostic and nothing came back. and today it started running hot. it seamed to cool down if i down shifted or gave it more gas. i've been struggling with this PLEASE HELP!! THANKS IN ADVANCE.