While electrodeposited antimony telluride thin films with silver contents demonstrated promising thermoelectric properties, their thermal conductivity and the silver content dependence remain unknown. Here, we report the thermal conductivities of Ag_3.9Sb_33.6Te_62.5 and AgSbTe₂ thin films with controlled annealing and temperature conditions and demonstrate the impact of silver content on thermal transport. After annealing at 160 °C, the room-temperature thermal conductivity of Ag_3.9Sb_33.6Te_62.5 and AgSbTe₂ thin films increases from 0.24 to 1.59 Wm^-1 K^-1 and from 0.17 to 0.56 Wm^-1 K^-1, respectively. Using phonon transport models and X-ray diffraction measurements, we attribute the thermal conductivity increases to the crystal growth and explain the thermal conductivity variations with the degree of crystallization. Unlike electrical properties reported in previous studies, the presence of silver contents has little impact on the thermal conductivity of Ag_3.9Sb_33.6Te_62.5 and leads to a strong reduction in the thermal conductivity of AgSbTe₂ thin films. By performing transient thermal conductivity measurements at 94 °C, we find the crystallization activation energy of Ag_3.9Sb_33.6Te_62.5 and AgSbTe₂ films as 1.14 eV and 1.16 eV, respectively. Their differences reveal the role of silver in inhibiting the nucleation and growth of Sb₂Te₃ crystals and impeding thermal transport. These findings provide guidance for optimizing doping and annealing conditions of antimony tellurides for near-room-temperature thermoelectric applications.