  We present a new grid of convective BL Herculis models using the
state-of-the-art 1D non-linear radial stellar pulsation tool MESA-RSP. We
investigate the impact of metallicity and four sets of different convection
parameters on multi-wavelength properties. Non-linear models were computed for
periods typical for BL Her stars, i.e. $1 \leq \mathrm{P (days)} \leq 4$
covering a wide range of input parameters - metallicity ($-2.0\; \mathrm{dex}
\leq \mathrm{[Fe/H]} \leq 0.0\; \mathrm{dex}$), stellar mass
(0.5M$_{\odot}$-0.8M$_{\odot}$), luminosity (50L$_{\odot}$-300L$_{\odot}$) and
effective temperature (full extent of the instability strip; in steps of 50K).
The total number of BL Her models with full-amplitude stable pulsations used in
this study is 10280 across the four sets of convection parameters. We obtain
their multiband ($UBVRIJHKLL'M$) light curves and derive new theoretical
period-luminosity ($PL$), period-Wesenheit ($PW$) and period-radius ($PR$)
relations at mean light. We find that the models computed with radiative
cooling show statistically similar slopes for $PL$, $PW$ and $PR$ relations.
Most empirical relations match well with the theoretical $PL$, $PW$ and $PR$
relations from the BL Her models computed using the four sets of convection
parameters. However, $PL$ slopes of the models with radiative cooling provide a
better match to empirical relations for BL Her stars in the LMC in the $HK_S$
bands. For each set of convection parameters, the effect of metallicity is
significant in $U$ and $B$-bands and negligible in infrared bands, which is
consistent with empirical results. No significant metallicity effects are seen
in the $PR$ relations.
