A silicon based hybrid plasmonic waveguide (HPW) configuration has been widely utilized to monitor the power flowing in the plasmonic circuit. Due to the approximately linear relationship between resistance and temperature change (the temperature coefficient of resistance, TCR), the voltage-signal variation directly leads to the change of resistance and the corresponding change of coupled-in power. However, the size effect is rarely explored and demonstrated, which plays a substantial role while the metal-strip thickness approaches to its electron mean free path. It exhibits different electric properties, such as reduced TCR and thermal conductivity, resulting in deviations of resistivity. On the contrary, due to the increase of boundary scattering and narrow-strip absorption, an improvement of the responsivity and excepted sensitivity is found. Therefore, considering a trade-off associated with size effects, 50 nm silver-strip and gold-strip were utilized as the conductor layer in the HPW configuration with different geometries, respectively. Meanwhile, a 50 nm x 300 nm gold-strip HPW provides an improvement performance, up to 13.7 mV mW V-1, 0.05 mu W sensitivity at bias 0.1 V. Its responsivity is about 1.4 times larger than that of silver, which contradicts to the macroscopic model.