Changes in atmospheric temperature are a fundamental measure of climate change. Microwave sounders have been monitoring global atmospheric temperatures since late 1978 by the Microwave Sounding Unit (MSU) and the Advanced Microwave Sounding Unit (AMSU). Unfortunately, these instruments are plagued by both time varying biases and by drifts in local measurement time with effects that must be characterized and removed before constructing a long-term dataset. We describe the methods we used to account for these challenges during the construction of the latest versions (V3.2) of the Remote Sensing Systems datasets. To assess the validity of the long-term changes in these data, we compare our results with those from homogenized radiosonde datasets. For global averages and northern extratropical averages of the lower tropospheric temperature anomalies we find that the satellite data and four recent adjusted radiosonde datasets are in excellent agreement once sampling errors are taken into account. In the tropics and the southern extratropics, where there are many fewer radiosonde stations, the agreement is not as good.