  Lensed quasars are powerful cosmic laboratories; they are used to
simultaneously probe various astrophysical phenomena. Microlensing by stars
within distant galaxies acts as strong gravitational lenses of multiply imaged
quasars, and provides a unique and direct measurement of the lensed quasar
internal structure. Microlensing of the continuum emitting region as well as
the broad-line region (BLR) is well characterized by four observable indices,
$\mu^{cont}$, $\mu^{BLR}$, $WCI$ (wing-core), and $RBI$ (red-blue), measured
directly from the spectra. During the 2004-2007 monitoring period, image A of
the quadruply lensed system Q2237+0305 underwent a strong microlensing
amplification, while image D remained unaffected. We used 35 epochs of archival
spectrophotometric data of Q2237+0305 obtained with the Very Large Telescope of
the European Southern Observatory to develop an independent microlensing method
for estimating the geometry and size of the BLR. We measured the index time
series for the CIV line and the continuum emission at $1450\,\unicode{x212B}$.
We built a library of the simulated microlensing index time series that
reproduce the observed times series based on three representative BLR models:
Keplerian disk (KD), polar wind (PW), and equatorial wind (EW). After sampling
the model parameter space, we find that KD is the predominant model, while PW
and EW are less likely. We infer that the system is viewed at an intermediate
viewing angle $i\sim 35^\circ$, and we estimate the most likely CIV BLR
half-light radius $r_\mathrm{1/2}=51\pm 23$ light days. Our results are in good
agreement with previous findings in the literature and extend the validity of
the index-based approach to a temporal domain.
