I am going to look at this differently.
a totally sealed box with 50% humidity at 70.0 deg F.
with no internal or external moisture variations, will return to exactly 50% humidity, when the box is brought back to exactly 70.0 deg F.
back to practicality. the heater should be so small as to take 5 minutes to raise the temperature in the box by 1 degree
and the humidifier should take 5 minutes to raise humidity by 1 percent.
you may think these to be extraordinarily long times, but if you can change the temperature by 1 degree in 1/2 second, you will need to slice that into hundreds in order to get any semblance of control.
the sizing of the device is critical to the successful operation.
think of an incubator. the egg breaths through the shell at such a slow pace that it might take a day to raise the humidity in that box. that means, a properly sized dehumidifier should be able to dehumidify 4 times faster than the process. or it should take 6 hours.
it is probably easier to control something larger than a shoe box or smaller than a box for copy paper.