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 thousand times faster than in a standard dc measurement. The achieved noise equivalent temperature of this first rf primary measurement is about 1 mK/$\sqrt{\rm Hz}$ at the bath temperature $T=200\,$mK.