The hot wire in a MAF is the sensor itself, it has a positive temperature coefficient so resistance increases as it gets hotter. These typically work by having two wires, one to measure the temperature of the air and the second, heated one to measure flow. They are wired in a Wheatstone bridge and the circuit maintains a fixed temperature difference between them by increasing or decreasing the hot wire current. This cancels out the temperature of the air, and the heater drive current required to do this is the output of the sensor.
Platinum wires are used as they are fairly linear and provide very fast response. Thermistors could be used but are horribly non-linear, so compensating ambient temperature would be more difficult. A better solution for a DIY sensor would be to use the Vf of a PN junction in a diode or transistor which has a linear, predictable temperature coefficient.