Most motors intended for variable speed operation will generate their max torque up to "base speed" which is typically 1500rpm for motors designed for 50Hz. Beyond that, they are typically capable of constant power until the back emf approaches the available voltage, beyond which point you need "field weakened" operation.
In the constant power region, the torque falls off as the speed rises, given that power = torque x speed. The speed range for constant power is rather limited for fairly conventional machines. Once you start looking at wider ranges of constant power speed, you need more complex and expensive inverters and control schemes. For instance, for a hybrid electric vehicle, the engine speed may be 1000-6000rpm, so designing a motor and inverter for that application is more challenging than for a machine tool spindle motor that may have a more limited range of operating speeds.
To answer the original query, you can buy fairly standard industrial motors that have an independently powered fan on the back end. In this way you can actually operate the motor with high torques and low speeds without overheating the motor. And many industrial motors will have a temperature sensor which will allow overtemperature protection amongst other things.
My lathe and milling machines both have variable speed drives but I generally try to get the speed range roughly right with the belt or gearbox and then modulate the speed around that set point. Trying to operate the motor much above or below its base speed would result in significantly limited power. In both cases the original motor power rating is fairly well selected for the application (and assumes the presence of a gearbox) so unless you want to pussy foot around, this is the only sensible way to shift respectable metal.
Muzzer