The ability to engineer the thermal conductivity of materials allows us to control the flow of heat and derive novel functionalities such as thermal rectification, thermal switching and thermal cloaking. While this could be achieved by making use of composites and metamaterials at bulk length-scales, engineering the thermal conductivity at micro- and nano-scale dimensions is considerably more challenging. In this work, we show that the local thermal conductivity along a single Si nanowire can be tuned to a desired value (between crystalline and amorphous limits) with high spatial resolution through selective helium ion irradiation with a well-controlled dose. The underlying mechanism is understood through molecular dynamics simulations and quantitative phonon-defect scattering rate analysis, where the behaviour of thermal conductivity with dose is attributed to the accumulation and agglomeration of scattering centres at lower doses. Beyond a threshold dose, a crystalline-amorphous transition was observed.