I have this issue...Usually the day after...Started a couple years ago...

I'm using Sidi Erog2's (so I got good shoes....that fit)
I use Specialized footbeds...

No hot spots on the bike, only after...

For me what I notice is that the burning seems to get worse as the day goes on at work and if I remove my shoes than it slowly subsides...So I have a pair of Birkenstock sandals at my desk that I slip on when it gets annoying...At home I just take off my socks...

I assume it's from the beating my feet take in carbon soled shoes riding over crappy Southern Ontario roads....

No biggie...I've just learned to live with it....

I'm not about to go switching shoes and/or footbeds since everything is fine on the bike....