First of all, thank you for your patient, we are solving cases as soon as possible.
I have run your attached project and effectively get the same results as the SDK example, although unfortunately I do not have a thermal insulated box nor a thermal camera. What I get is a reading of about 42°C while the ambient temperature is 26/27°C.
Now, as it mentions in the reference manual the TEMPMON determine the on-die operational temperature, which, according to our application team, is approximately equal to the junction temperature. The latter, in operation, is higher than the temperature of the case and the temperature of the outside of the part.
Regarding the temperature difference between the custom and evaluation boards, have you taken a look at the processor's power consumption on your board? I want to make sure there isn't actually an issue that is causing them to draw more current which would also cause the die to heat.
And just as an extra fact, we have no report of any errata regarding the RT1064 TEMPMON.
Hope it help you to explain your results.