During the past few years, there has been a flurry of investigations on the lattice thermal transport of three-dimensional (3D) graphene, however, few studies have detailed how to adjust this property effectively using the presently available engineering technologies. In this work, the thermal transport properties of a porous single layer carbon honeycomb (SL-dCHC-2) and its mechanical response are systematically studied. We show that the thermal conductivity of SL-dCHC-2 can be adjusted effectively by varying the tensile strain, and its value is enhanced by up to 11.3 times with 8% strain as compared to the unstrained case. This value is significantly larger than what was observed for other two-dimensional (2D) materials such as silicene (∼7 times larger). This outstanding behavior is explained by the phonon mode level, indicating that a profound increase of the thermal conductivity under tensile strain is attributed to the enhancement of the phonon lifetime. In addition, the trend for the root mean squared displacement, which is closely related to the phonon anharmonic effect, correlates with the non-monotonic response of the dimerized C-C bonds at the linkage of the structure. These investigations and obtained results provide important guidance to develop 3D carbon honeycombs for several different purposes, such as for use as molecular sieves and in water purification applications.