Carbon nanodots (C-dots) are nanometer-sized particles of amorphous carbon that form highly stable water-based suspension if given the right surface treatment. Their size, stability and unique photoluminescent properties make them attractive candidates for tracer materials for use in heat transfer experiments. Here we measure the effective thermal conductivity of water containing 1.5 g/L (0.077% volume fraction) of fluorescent green carbon nanodots. In conflict with empirical predictions from nano-fluid literature but consistent with predictions from classical theories applied to nanofluid thermal conductivity enhancement, the results show no measurable difference between the thermal conductivity of the colloid and deionized water. This finding adds confirmation to the value of photoluminescent carbon nanodots for use as a water tracer in bench-top heat transfer experiments.