I visited the National Palace Museum in Taipei, Taiwan yesterday. All the display cases contain an electronic temperature/RH meter. I assume that they are accurate, considering that most of the objects are many centuries old (some a few thousand years old), and that this is a museum.
The average temperature in the cases was between 21 to 22 degC, and the average relative humidity was between 57% and 61%, even in cases containing wooden artifacts. This was so regardless of the age of the wooden artifacts. The simple conclusion to draw from this is that the micro-climate for pianos should be similar.