Free liquid-jet impingement is well researched due to its high heat transfer ability and ease of implementation. This study considers both the steady state and transient heating of a patterned plate under slot-free-liquid jet impingement. The primary working fluid was water (H2O) and the plate material considered was silicon. Calculations were done for Reynolds number (Re) ranging from 500 to 1000 and indentation depths from 0.000125 to 0.0005 m for three different surface configurations. The effect of using different plate materials and R-134a as the working fluid were explored for the rectangular step case. The distributions of the local and average heat-transfer coefficient and the local and average Nusselt number were calculated for each case. A numerical model based in the FIDAP computer code was created to solve the conjugate heat transfer problem. The model used was developed for Cartesian coordinates for both steady state and transient conditions. Results show that the addition of surface geometry alters the fluid flow and heat transfer values. The highest heat-transfer coefficients occur at points where the fluid flow interacts with the surface geometry. The lowest heat-transfer coefficients are found in the indentations between the changes in geometry. The jet velocity has a large impact on the heat transfer values for all cases, with increasing jet velocity showing increased local heat-transfer coefficients and Nusselt number. It is observed that increasing the indentation depth for the rectangular and sinusoidal surfaces leads to a decrease in local heat transfer whereas for triangular patterns, a higher depth results in higher heat-transfer coefficient. The transient analysis showed that changing surface geometry had little effect on the time required to reach steady state. The selection of plate material has an impact on both the final maximum temperatures and the time required to reach steady state, with both traits being tied to the thermal diffusivity (α) of the material.