  We present new theoretical period-luminosity (PL) and period-Wesenheit (PW)
relations for a fine grid of convective BL Her, the shortest period T2Cs,
models computed using MESA-RSP and compare our results with the empirical
relations from Gaia DR3. We use the state-of-the-art 1D non-linear radial
stellar pulsation tool MESA-RSP to compute models of BL Her stars over a wide
range of input parameters - metallicity (-2.0 dex $\leq$ [Fe/H] $\leq$ 0.0
dex), stellar mass (0.5M$_{\odot}$-0.8M$_{\odot}$), stellar luminosity
(50L$_{\odot}$-300L$_{\odot}$) and effective temperature (full extent of the
instability strip; in steps of 50K). The BL Her stars in the All Sky region
exhibit statistically different PL slopes compared to the theoretical PL slopes
computed using the four sets of convection parameters. We find the empirical PL
and PW slopes from BL Her stars in the Magellanic Clouds to be statistically
consistent with the theoretical relations computed using the different
convection parameter sets in the Gaia passbands. There is negligible effect of
metallicity on the PL relations in the individual Gaia passbands. However,
there exists a small but significant negative coefficient of metallicity in the
PWZ relations for the BL Her models using the four sets of convection
parameters. This could be attributed to the increased sensitivity of bolometric
corrections to metallicities at wavelengths shorter than the V band. Our BL Her
models also suggest a dependence of the mass-luminosity relation on
metallicity. We found the observed Fourier parameter space to be covered well
by our models. Higher mass models (> 0.6M$_{\odot}$) may be needed to reliably
model the observed light curves of BL Her stars in the All Sky region. We also
found the theoretical light curve structures (especially the Fourier amplitude
parameters) to be affected by the choice of convection parameters.
