The maximum current that an overhead transmission line can continuously carry depends on external weather conditions, most commonly obtained from real-time streaming weather sensors. The accuracy of the sensor data is very important in order to avoid problems such as overheating. Furthermore, faulty sensor readings may cause operators to limit or even stop the energy production from renewable sources in radial networks. This paper presents a method for detecting and replacing sequences of consecutive faulty data originating from streaming weather sensors. The method is based on a combination of (a) a set of constraints obtained from derivatives in consecutive data, and (b) association rules that are automatically generated from historical data. In smart grids, a large amount of historical data from different weather stations are available but rarely used. In this work, we show that mining and analyzing this historical data provides valuable information that can be used for detecting and replacing faulty sensor readings. We compare the result of the proposed method against the exponentially weighted moving average and vector autoregression models. Experiments on data sets with real and synthetic errors demonstrate the good performance of the proposed method for monitoring weather sensors.