This paper summarizes our recent work on the development of thermal anemometry to measure velocity and temperature fluctuations in oscillating flows. First, we demonstrate that velocity cannot be measured accurately by hot-wire anemometry in oscillating flows when the flow reverses its direction. Indeed, there is no unique and well-defined correlation between the flow velocity and heat transfer near flow reversal, which prevents the recovery of velocity fluctuations from the anemometer signal. Second, we detail new procedures for the measurement of temperature fluctuations in oscillating flows using cold-wire thermometry. Thermal inertia alters the response of the sensor to temperature changes. The thermal inertia of the cold-wire (operated by a constant-current or a constant-voltage anemometer) is corrected instantaneously using the same wire but in the heated mode (operated by a constant-voltage anemometer). The new procedures are validated in an acoustic standing-wave where temperature fluctuations amplitudes lower than 0.2K at approximately 1000Hz are successfully measured. Experiments near the edges of the stack in a thermoacoustic refrigerator demonstrate the nonlinearity of the temperature field.