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We present a scheme and demonstrate measurements of a Coulomb-blockade thermometer (CBT) in a microwave-transmission setup. The sensor is embedded in an LCR resonator, where R is determined by the conductance of the junction array of the CBT. A transmission measurement yields a signal that is directly proportional to the conductance of the CBT, thus enabling the calibration-free operation of the thermometer. This is verified by measuring an identical sensor simultaneously in the usual dc setup. The important advantage of the rf measurement is its speed: the whole bias dependence of the CBT conductance can now be measured in a time of about 100 ms, which is 1000 times faster than in a standard dc measurement. The achieved noise-equivalent temperature of this rf primary measurement is about 1mK/Hz at the bath temperature T=200mK.