The objective of this paper is to understand the limits on the response time generated by the thermal dynamics of the Martian wind sensor of the MEDA instrument, working under Constant Temperature Operation (CTO). This technology has been flown aboard the Mars Science Laboratory, InSight, and Mars 2020. It will be shown that active control thermal anemometry enables a time response to wind fluctuations faster than the time constants defined by the thermal inertia of the sensor components. It will also be shown that the temperature redistributions on the temperature-uncontrolled parts of the supporting structure impose a limit on the bandwidth of the sensor. We present a model of the MEDA hot film anemometers describing what parameters control their dynamical response, why wind tunnel testing confirmed them to be faster than 1 s, and criteria to select materials that reduce the response time to approach 0.2 s.