What is the primary function of the nucleus in a cell?

The primary function of the nucleus in a cell is to store chromatin. Chromatin is a complex of DNA and protein that forms the genetic material found within the nucleus. The nucleus houses the cell's genetic material, which contains the instructions necessary for the growth, development, and functioning of the organism. By storing chromatin safely within a membrane-bound compartment, the nucleus ensures that the genetic information is protected from the various processes occurring in the cytoplasm of the cell.

This genetic material plays a crucial role in the regulation of gene expression and is essential for DNA replication during cell division. The nucleus also coordinates cellular activities such as metabolism, growth, and reproduction by controlling the synthesis of RNA and ultimately, proteins.

The other options represent functions that pertain to different cellular components. For instance, the production of energy takes place in the mitochondria, not the nucleus. Temperature regulation is typically a function of the organism as a whole rather than an individual cell, and protein synthesis occurs primarily in the ribosomes located in the cytoplasm. Thus, the nucleus's core role of storing and protecting chromatin distinctly sets it apart from these other cellular functions.