What you are trying to describe is transcription, the process of reading a DNA template to produce a RNA transcript. This is done in the nucleus for eukaryotes,

What you are trying to describe is transcription, the process of reading a DNA template to produce a RNA transcript. This is done in the nucleus for eukaryotes, and in the nucleoid for prokaryotes (which don't have a nucleus). RNA Polymerase is the protein that synthesizes mRNA (from the DNA template) and the nitrogenous base Uracil (U) is used in place of Thymine (neither are proteins). In fact Uracil is less stable that Thymine and the hypothesis is that DNA uses Thymine due to its lower rate of point mutation. (Note I mean less stable in the sense that it can be mutated more easily due to functional groups).