Which factors besides the thermodynamic stability are important for the hairpin in intrinsic transcription termination?
The RNA hairpin transcription terminator in prokaryotes is terminated by the GC rich hairpin followed by 4+ uracil bases as you describe it.  

The original reference describing the hairpin, described the sequence requirements as being for the thermodynamic stability of the hairpin, but the protein nusA has also been found to stimulate termination.  

You might think that there would be some protein that would precisely bind this motif and mediate the termination, but at least as far as I can find, it appears that the hairpin clogs up the polymerase itself, causing termination.  This review linked here has some nice pictures of the RNAP bindig pocket model.