No. The surrounding temperature has little effect on the Hall current.
You use a thermistor for temperature sensing.
The Hall probe consists of a thin rectangular plate made of a semiconductor material. The plate has four electrical contacts with ohmic contact. Two out of them are called biasing contacts, through which the biasing current flows. The other two contacts are called sense contacts at right angle to the biaising contacts; their function is to measure the Hall voltage.
The magnetic field traverses the plate - the biasing current is deflected by the magnetic field causing a Hall voltage to appear on the sensing contacts.
You only see the Hall current which is proportional to the strength of the magnetic field.
Yes I know, you could use a thermistor, a thermocouple or even a platinum resistor. However, this involves trying to thread yet more wires into the hub and then trying to find a good place to attach the sensor and then hope it doesn't fall off in use.
So, if we can utilise what is already inside the motor, it's a significant advantage.
I wasn't specifically thinking about measuring a Hall current.
The Hall voltage is = IB/nte
Where I is the current passing through the sensor, B is the magnetic field, n is the charge carrier density, t is the thickness of the material and e is the atomic unit of charge. The situation with semiconductors is slightly more complicated as you have holes and electrons, and these have different mobilities.
B is dependent on temperature, as increased temperature reduces the strength of the magnetic field.
I will change with temperature, as in semiconductors, resistance tends to drop with increasing temperature.
t will change slightly with temperature, as materials often expand when heated, but this may be too small to be significant.
n will change with temperature, as in semiconductors there are usually more charge carriers available at a higher temperature.
e is constant.
So you can see, there are several parameters related to the Hall voltage that have a temperature dependency.
Now, the Hall "sensors" we have in our motors are not really sensors, they are Hall switches. Inside they will have a Hall sensor which triggers another circuit to activate a "switch". That "switch" will be some form of transistor, i.e. another semiconductor, whose electrical properties are dependent on temperature.
I can imagine it may be possible to measure temperature with these Hall switches using different strategies.
One could be just monitoring the current flowing in the Hall switch circuit and seeing how this varies with motor temperature. Higher temperature should lead to a slight increase in current in this circuit.
Another method may be looking at the rise time of the switch with temperature. Since the Hall voltage is temperature dependent, the speed at which the charges can separate and reach the opposing sides of the sensor will vary accordingly. This means the switch will take longer or shorter to transition from conducting to non conducting and back again according to the temperature.
As you know the motor RPM, you could even look at how long the switch should be on and off and then measure the on/off pulse width.
These are just a few thoughts I had going through my mind cycling home. I'm sure there are probably many more ways of doing this.