I want to halve a cream cheese cake recipe, how do I adjust the pan size, so I can keep the same cake height?

Assuming you're baking in a round pan: The volume of a cylinder is pi * r^2 * h. You halve the volume and want to keep the height the same. That means you want to scale the radius of the pan by a factor of 1/sqrt(2). So for example, if the recipe is intended for a pan of diameter 25 cm it has radius 12.5 cm and you want to use a pan with radius 12.5*(1/sqrt(2))=8.8 cm, or diameter approximately 17.6 cm.

Adjusting the baking temperature and time is a bit trickier. I would start by lowering the temperature by about 25 degrees Celsius and start checking the cake with a pick about 15 minutes before the stated time in the recipe.