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We explore steady state and transient heat transfer from a narrow, rectangular stainless steel heater strip cooled from one side by an open bath of He~II. Setup validation is done by fitting the Kapitza heat transfer expression $Q = a_\mathrm{K} \left( {T_\mathrm{s}}^{n_\mathrm{K}} - {T_\mathrm{b}}^{n_\mathrm{K}} \right)$ to steady state measurements, finding fit parameters within the expected range; $a_\mathrm{K}$ = 1316.8$\pm10\%$ $\mathrm{W}\mathrm{m}^{-2}\mathrm{K}^{-1}$, $n_\mathrm{K}$ = 2.528$\pm10\%$. We find critical heat flux in line with estimates from literature, and the time between a step in heating and the onset of film boiling follows the expected $\propto Q^{-4}$ dependence. During the first millisecond after a step in applied heating power density our measurements show a slower thermal rise time than that found by a time-dependent one-dimensional model of our setup using the steady state Kapitza heat transfer expression as the cooling boundary condition. However, the results compare favourably with transient measurements in literature. After the first millisecond, agreement between measurement and model is excellent. We do not find conclusive evidence of an orientation dependence of the Kapitza heat transfer mechanism, nor heat transfer differences that can be attributed to local surface variations along the same heater.