Temperature is usually the first filter when choosing between the four common permanent magnet materials, because they differ in heat behaviour far more than in almost anything else. Picking by price or by strength alone is how a magnet ends up in a motor that is simply too hot for it.
Neodymium (NdFeB): the strongest, with a limited heat range
Neodymium gives the most force for the least volume. Standard grades are suited to roughly 80°C; special high-temperature grades extend that to around 200°C, at the price of some strength. Like all magnets, its output dips as it warms (a reversible loss of roughly a tenth of a percent per degree), and beyond the grade's limit part of that loss becomes permanent. It also needs a coating to resist corrosion.
Samarium cobalt (SmCo): weaker, but steady when hot
At room temperature SmCo is not as strong as neodymium, but it holds its strength much better as the temperature rises and works up to about 350°C. It resists corrosion without a coating. The trade-offs are higher cost and brittleness. It is the usual answer for hot servo motors and sensors.
AlNiCo: the highest temperature, the lowest resistance to demagnetization
AlNiCo tolerates temperatures up to about 500°C and its strength changes very little with heat. Its weakness is the opposite: it can be weakened by a reverse magnetic field, or even by careless handling against steel. That is why it is usually made long and slender, and why it is found in measuring instruments and sensors rather than in holding applications.
Ferrite: cheap, corrosion-proof, weakest
Ferrite (ceramic) is the lowest-cost option, needs no coating and works up to about 250°C, but gives the least force per volume. Unusually, it becomes more vulnerable to demagnetization in the cold, not in the heat, so a low operating temperature matters for it.
How to choose
Write down the real minimum and maximum temperature at the magnet's location in the assembly, not the room temperature. Then pick the lowest-cost material that works with a safety margin. If you tell us that range and what the magnet has to do, we will recommend the material and grade.