mercury missing when hot

[barbwire44]

I have a problem my mercury 70 outboard runs fine cold, but this weekend after a short run it began to miss, then I shut it off waited a few minutes fired it back up ran great for about 200 yards then started sputtering and missing again, so let it set a few minutes and the same thing, went back to the dock waited a few hours fired it back up ran great for 5 minutes then started the same thing all over, runs great cold , but once warm it misses badly. I was told this is most likely the switch box???? What do you guys think??