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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 empiricalrelations from Gaia DR3. We use the state-of-the-art 1D non-linear radialstellar pulsation tool MESA-RSP to compute models of BL Her stars over a widerange of input parameters - metallicity (-2.0 dex $\leq$ [Fe/H] $\leq$ 0.0dex), stellar mass (0.5M$_{\odot}$-0.8M$_{\odot}$), stellar luminosity(50L$_{\odot}$-300L$_{\odot}$) and effective temperature (full extent of theinstability strip; in steps of 50K). The BL Her stars in the All Sky regionexhibit statistically different PL slopes compared to the theoretical PL slopescomputed using the four sets of convection parameters. We find the empirical PLand PW slopes from BL Her stars in the Magellanic Clouds to be statisticallyconsistent with the theoretical relations computed using the differentconvection parameter sets in the Gaia passbands. There is negligible effect ofmetallicity on the PL relations in the individual Gaia passbands. However,there exists a small but significant negative coefficient of metallicity in thePWZ relations for the BL Her models using the four sets of convectionparameters. This could be attributed to the increased sensitivity of bolometriccorrections to metallicities at wavelengths shorter than the V band. Our BL Hermodels also suggest a dependence of the mass-luminosity relation onmetallicity. We found the observed Fourier parameter space to be covered wellby our models. Higher mass models (> 0.6M$_{\odot}$) may be needed to reliablymodel the observed light curves of BL Her stars in the All Sky region. We alsofound the theoretical light curve structures (especially the Fourier amplitudeparameters) to be affected by the choice of convection parameters.

A theoretical framework for BL Her stars -- II. New period-luminosity relations in the Gaia passbands