Graphene has been highlighted as a great potential material in wearable devices, owing to its extraordinary properties such as mechanical softness, high electrical conductivity and ultra-thin thickness. However, there are remaining challenges in thermal dissipation of graphene under such complicated conditions, which significantly affect the performance of portable electronics. Using molecular dynamics simulations, we have performed systematic analysis of thermal performance for the application in wearable devices in terms of graphene with defects, under uniaxial tensile strain, and vertical stress. Three kinds morphology of defects (horizontal line defect, circular defect, and vertical line defect) are constructed by deleting atoms on the pristine graphene plane. The thermal conductivity is related to the projected defected area perpendicular to the direction of the heat current. The relative thermal conductivity displays a cubic decreasing trend with the increase of uniaxial tensile strain. Besides, the thermal conductivity of graphene is not only related to the deformation quantity, but also related to the type of compression region. Our results show that the thermal conductivity decreases a lot under local stress with larger vertical deformation, while no obvious decline is observed under the global stress. This study aims to provide guidelines and ballpark estimates for experimentalists fabricating flexible devices from graphene.