The glassy state of zeolitic imidazolate frameworks (ZIFs) has shown great potential for energy-related applications, including solid electrolytes. However, their thermal conductivity (κ), an essential parameter influencing thermal dissipation, remains largely unexplored. In this work, using a combination of experiments, atomistic simulations, and lattice dynamics calculations, we investigate κ and the underlying heat conduction mechanism in ZIF glasses with varying ratios of imidazolate (Im) to benzimidazolate (bIm) linkers. The substitution of bIm for Im tunes the node-linker couplings but exhibits only a minor impact on the average diffusivity of low-frequency lattice modes. On the other hand, the linker substitution induces significant volume expansion, which, in turn, suppresses the contributions from lattice vibrations to κ, leading to decreased total heat conduction. Furthermore, spatial localization of internal high-frequency linker vibrations is promoted upon substitution, reducing their mode diffusivities. This is ascribed to structural deformations of the bIm units in the glasses. Our work unveils the detailed influences of linker substitution on the dual heat conduction characteristics of ZIF glasses and guides the κ regulation of related hybrid materials in practical applications.