Yep, the soles just aren't stiff enough and your foot is flexing overly much on the pedals. I cycled with similar shoes when I first learned how to ride this past winter and I just got used to foot pain. I clip in these days and that has removed most of the discomfort.
It did help me, however, to wear uncleated cycling shoes on my BMX pedals - I wore Keen Commuters - and while they are really not stiff enough to use with cleats (for me) they are stiffer than the usual running shoe and I had much less of problem with hot foot than I did with regular running shoes.



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