Thermal conductivity measurement techniques for materials with nanoscale dimensions require fabrication of very complicated devices or their applicability is limited to a class of materials. Discovery of new methods with high thermal sensitivity are required for the widespread use of thermal conductivity measurements in characterizing materials' properties. We propose and demonstrate a simple non-destructive method with superior thermal sensitivity to measure the in-plane thermal conductivity of nanosheets and nanowires using the bolometric effect. The method utilizes laser beam heating to create a temperature gradient, as small as a fraction of a Kelvin, over the suspended section of the nanomaterial with electrical contacts. Local temperature rise due to the laser irradiation alters the electrical resistance of the device, which can be measured precisely. This resistance change is then used to extract the temperature profile along the nanomaterial using thermal conductivity as a fitting parameter. We measured the thermal conductivity of V 2 O 3 nanosheets to validate the applicability of the method and found an excellent agreement with the literature. Further, we measured the thermal conductivity of metallic 2H-TaS 2 for the first time and performed ab initio calculations to support our measurements. Finally, we discussed the applicability of the method on semiconducting nanosheets and performed measurements on WS 2 and MoS 2 thin flakes.