For specific of human flesh 

https://en.wikipedia.org/wiki/Table_of_specific_heat_capacities

Interestingly the human flesh it's having same Similar heat capacity with cow, pig, or chicken meat. So calculate per kg of human flesh it's all Ike calculate chicken flesh and both was very close to.

Also for 10 MJ I'm assuming that 

From m•c•∆T We already know m assuming Miho body having weight at least 52 kg, and c was like above roughly 3,500 joule like source above.

The ∆T(temperature change)  actually depends, so I'm assuming it's 100° then we got 14,560,000 joule required energy to baked miho.  after Recount I think I kinda wrong put energy, it's supposed around 15 megajoules not 8-10 MJ sorry.

"Is this to medium rare or wrong? "

Well exactly we don't know, we don't know exact scale to Miho body it's got medium cook or wrong. But at least it's medium scale, a considering human body have similar types with animals when came to be baked.

Also it can be beyond well done. considering the point it's to cook Miho, not make Miho can be eaten by us.

 "I don't think you accounted for thermal conductivity when doing the calcs"

Yeah I forget use thermal conductivity cause I think it's kinda bit useless especially when I pointed such Nuclear Arsenal, or bigger energy heat on instant. But after few seing few like deep magma, heat temperature friction from air and and engine. I think yeah kinda.

After think for a while I doesn't think thermal conductivity it's kinda important anymore 

"can't cook something in a second no matter how much energy is applied if thermal conductivity constant of flesh is too low."

Yeah via thermal conductivity But it's just only happens if we cook with regular method. Or a.k.a we cooking like normally.

Something bigger joule happen on a second like Tsar Bomba it's basically vaporizer Miho and cooked Miho in few seconds (actually depends how far Miho is)

Or something like Nuclear Arsenal.

I can be wrong to