  Quantum spin ice (QSI) is an emblematic three-dimensional $U(1)$ quantum spin
liquid (QSL) on the pyrochlore lattice that hosts gapless photon-like modes and
spinon excitations. Despite its notable status and the current rise of strong
material candidates Ce$_2$(Zr, Sn, Hf)$_2$O$_7$, there are still only a few
analytical approaches to model the low-energy behavior of QSI. These analytical
methods are essential to gain insight into the physical interpretation of
measurements. We here introduce the self-consistent exclusive boson
representation (SCEBR) to model emergent spinon excitations in QSI. By treating
the presence of other emergent charges in an average way, the SCEBR extends the
range of validity of the exclusive boson representation previously introduced
by Hao, Day, and Gingras [Hao, Day, and Gingras, Physical Review B, 90, 214430
(2014)] to numerous cases of physical relevance. We extensively benchmark the
approach and provide detailed analytical expressions for the spinon dispersion,
the Bogoliubov transformation that diagonalizes the system, and the dynamical
spin structure factor for 0- and $\pi$-flux QSI. Finite temperature properties
are further investigated to highlight essential differences between the
thermodynamic behavior of the 0- and $\pi$-flux phases. We notably show that
the SCEBR predicts a reduction of the spinon bandwidth with increasing
temperature, consistent with previous quantum Monte-Carlo results, through
suppression of spinon hopping by thermal occupation. The SCEBR thus provides a
powerful analytical tool to interpret experiments on current and future
candidate material that has several advantages over other widely used methods.
