The reason you are assuming Is correct that on Changing the temperature the magnetic field is going to change as well in both permanent magnets and electromagnets now understand the reason behind this and let's make it more theory oriented as well.
First of all you should be aware of the terms drift velocity and relaxation time of the electrons I'll assume that you are!
So when there is change in temperature then there must be transfer of heat between the conductor and the surroundings and let's say the conductor is at the lower temperature than the surroundings then what will happen the heat will travel from surroundings to our conductor and this energy will get converted into the kinetic energy of the electrons (there is already some velocity in the electrons but as the temperature difference becomes bigger the heat energy will more and more get converted into the kinetic energy). So this will result in more collisions with their vacancies, other atoms and other free electrons and with this the electrons under the influence of the electric force because of the closed circuit (potential difference is applied) will not be able to totally decelerate the electrons earlier and change the direction of velocity quickly as it was doing before which were moving in the direction of electric field (in general they should move opposite to the direction of electric field because they are negatively charged but because of these more strong collisions this will deflect the electrons from the direction in which they should actually move, not significantly but yes, electron will gain more velocity in the direction of electric field as compared to normal conditions) will result in the decrement of the drift velocity and current as well because current and drift velocity are directly related to each other according to the equation $I = V_d enA$ Where $V_d$ is drift velocity and remaining are the constants.
Now let us understand with this equation:-
$R = \frac{ml}{ne^2τA}$
Just focusing $τ$ here is the relaxation time, and $n$ is the number of free electrons per unit volume.
From the above equation keeping all the constants beside such as length, area, mass and charge of an electron we can see that the resistance is inversely proportional to the relaxation time and the $n$ As the temperature increases the number of free electrons increases as well but there is not significant increase because there are already enough free electrons inside the conductor. And the main reason to increase the resistance here is the decrement in the relaxation time of the electrons because of increased velocity in random directions of the electrons due to conversion of the thermal energy. So this is how the resistance increases with increase in temperature and according to the ohms law i.e $V = IR$ the resistance increases which will lead to decrement in current and as the current is directly proportional to the magnetic field strenght hence it will decrease as well.
Hope it helps. 780