  We consider the question: Is it possible to measure two temperatures
simultaneously using a single thermometer? Under common circumstances, where
the thermometer can interact with only one bath at a time and the interaction
leads to complete thermalization, this is clearly impossible because the final
state of the thermometer would be independent of the temperature of the first
bath. In this work, we show that this task can indeed be accomplished with the
assistance of quantum control. In particular, we consider a composite particle
with multiple quantum degrees of freedom (DoF) as a temperature sensor, where
one of the DoF -- termed as internal DoF -- is susceptible to the local
temperature, thereby functioning as a thermometer, whereas another DoF --
termed external DoF -- is quantum-controlled. We leverage the entanglement
between the aforementioned DoF in a composite particle for two-temperature
thermometry by preparing the external DoF in a quantum superposition, exposing
the internal DoF to two local temperatures. We show that such a particle used
in a Mach-Zehnder type interferometer, or a quantum switch -- which allows
quantum control over the order of application of quantum channels -- can be
used to estimate two temperatures simultaneously, thus affirming our main
proposition. For each of these setups, we obtain the variance in the estimated
temperatures through the multi-parameter Cram\'er-Rao bound, and compare their
performances based on the range of total variance of the two temperatures
estimated. On benchmarking all the setups based on the total variance of the
estimated temperatures, we find that a quantum switch with a qudit probe
outperforms other setups. On restricting our probe to be a qubit, we find that
quantum switch performs equally well as a Mach-Zehnder type interferometer.
