MAF is not affected by the density of the air. The IAT feeds the ECU data which compensates for density.

A hot wire mass airflow sensor determines the mass of air flowing into the engine’s air intake system. The theory of operation of the hot wire mass airflow sensor is similar to that of the hot wire anemometer (which determines air velocity). This is achieved by heating a wire with an electric current that is suspended in the engine’s air stream, like a toaster wire. The wire's electrical resistance increases as the wire’s temperature increases, which limits electrical current flowing through the circuit. When air flows past the wire, the wire cools, decreasing its resistance, which in turn allows more current to flow through the circuit. As more current flows, the wire’s temperature increases until the resistance reaches equilibrium again. The amount of current required to maintain the wire’s temperature is directly proportional to the mass of air flowing past the wire. The integrated electronic circuit converts the measurement of current into a voltage signal which is sent to the ECU.

If air density increases due to pressure increase or temperature drop, but the air volume remains constant, the denser air will remove more heat from the wire indicating a higher mass airflow. Unlike the vane meter's paddle sensing element, the hot wire responds directly to air density. This sensor's capabilities are well suited to support the gasoline combustion process which fundamentally responds to air mass, not air volume. (See stoichiometry.)

Some of the benefits of a hot-wire MAF compared to the older style vane meter are:

responds very quickly to changes in air flow
low airflow restriction
smaller overall package
less sensitive to mounting location and orientation
no moving parts improve its durability
less expensive
separate temperature and pressure sensors are not required (to determine air mass)

There are some drawbacks:

dirt and oil can contaminate the hot-wire deteriorating its accuracy
installation requires a laminar flow across the hot-wire

The Mass Air Flow (MAF) sensor senses the amount of incoming air (Volume) into the engine. This sensor does not regulate the incoming air, this is done by the engine throttle plates.

The HOT WIRE MAF sensor is a fully electronic unit. It senses the amount of air flow into the engine by measuring the amount of current needed to maintain a constant temperature through a very thin (70 micrometers) platinum hot wire. Hence the name hot wire MAF sensor. It also measures air by weight, since it takes into consideration the air temperature as well.

This sensor works as follows. As the air enters the intake manifold through the hot wire MAF sensor it cools down the platinum wire, which is heated at a very precise temperature. When the MAF circuitry senses the platinum wire cooling down it increases the amount of current flow through the hot wire trying to maintain a specific temperature. This varying current flow is then converted to a voltage output signal by the MAF electronic circuitry and is used as an air flow indicator by the ECM. Hot wire MAF sensors have a signal that is directly proportional to air flow. So as air flow increases so does its voltage signal output.