  Exploring the limits of spontaneous emission coupling is not only one of the
central goals in the development of nanolasers, it is also highly relevant
regarding future large-scale photonic integration requiring energy-efficient
coherent light sources with a small footprint. These studies are accompanied by
a vivid debate on how to prove and interpret lasing in the high-$\beta$ regime.
We investigate close-to-ideal spontaneous emission coupling in GaN nanobeam
lasers grown on silicon. Due to their high optical quality, such nanobeam
cavities allow for efficient funneling of spontaneous emission from the quantum
well gain material into the laser mode. By performing a comprehensive optical
and quantum-optical characterization, supported by microscopic modeling of the
nanolasers, we identify high-$\beta$ lasing at room temperature and show a
lasing transition in the absence of a threshold nonlinearity at 156 K. This
peculiar characteristic is explained in terms of a temperature and excitation
power dependent interplay between 0D and 2D gain contributions.
