Thermal conductivity is a key property of oxide glass, especially for building applications such as thermal insulation materials and windows or glazed facades. However, this property is difficult to be predicted since it depends on several factors such as the degree of order/disorder and porosity. Here, we report on the effects of crystallization, crystalline phase, and crystal size on the thermal conductivity of a melt-quenched silicate glass. These effects were studied by heat-treating the glass at the onset crystallization temperature for different durations to vary crystallinity in the samples. The results show a general increase in thermal conductivity with crystallinity and crystal size in the nano-range (<75 nm). The growth of devitrite and combeite phases in the glass has a great impact on the thermal conductivity. Interestingly, an anomaly of thermal conductivity is found, i.e., the thermal conductivity of the sample with a relatively low crystallinity of <15 % is reduced by >20 % compared to that of the pure glass phase. This may be attributed to the grain boundaries between amorphous and crystalline phases, which scatter the phonons and thus reduce the thermal conductivity. These results imply that nano-crystallization in window glass might be a useful way to reduce the heat loss from glazed facades in the building envelope.