Experimental measurement of thermal conductivity is considered the most reliable tool for the study of phonon transport in ultra-thin silicon structures. While there has been a great success in thermal conductivity measurement of ultra-thin silicon layers down to 20 nm over the past decade, it is not clear if the existing techniques and tools can be extended to the measurements of sun 100 Angstrom layers. In this paper, an analytical study of the feasibility of electrical Joule heating and thermometry in patterned metal bridges is presented. It is concluded that thermal conductivity of silicon layers as thin as 5 nm can be obtained (uncertainty 20%) by performing steady-state measurements using an on-substrate nanoheater structure. The thermal characterization of silicon layers as thin as 1 nm may be possible using frequency domain measurements.