Assume it is an asynchronous induction motor (brush-less) with integrated cooling fan. If it becomes too hot, is it overloaded? Measure current.
Other reasons can be partly burnt windings, if capacitors are used for start-up and phase correction can they be dry or shortcut. Unusual smell and sound are indicating these types of errors.
An induction motor during same load have almost same heat-loss at 200 or 230 Volt AC.
Unloaded is heat-loss ~1.32 times higher (230/200)². As this is unloaded and with max rpm at cooling fan should it not be any problem.
Max rpm is mainly depending on frequency and number of poles, not voltage. Magnetic saturation increases heat which can be caused by over-voltage, but is not likely in this case.
I do not recommend to use a motor beyond its marking plate. Isolation is for example a security aspect that is voltage depending. Windings are designed for a certain max current and overload or start can cause too heavy peak current and reduced efficiency.
Voltage can vary quite wide for this type of motor while it can maintain almost same performance. Previously could you find motor-plates saying 220VAC +/- 10%. Nowadays is it rather common with this type of markings:
AJVS 1-phase-motor-208-240-v-50-60-Hz
Main data for this motor remains similar for 200-240 V (± 5 %) 50 Hz or even when switching from 50-60Hz, except that rpm increases.
Using a lamp dimmer for controlling an inductive engine is a way to increase heat in the coils of the engine and in worst case burn some windings. For a certain RPM and load is a average amount of power needed. A dimmer cuts out a part of every 50 Hz period which increases peak current during remaining time, resulting in higher peak current and increased resistive losses in the motor. Also magnetic saturation is a likely problem when current goes 200% above what the motor is designed for, producing a lot of heat.
For an inductive motor, the only simple way I know about to adjust heat dissipation (optimize efficiency) for a certain load is to use a frequency inverter.
Avoid unstable serial loads if you not is really sure about what you are doing. Serial resistors occurs in some rare cases to reduce start current in elevators, both parallel and serial capacitors are common as phase correctors but avoid serial inductors as it increases inductive load and can cause arcs over mains switch when powering off. At 0.65H/1A can you assume mains switch as something for onetime use, including parts of surrounding wall
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If market-plate says your voltage is too high, and you want to reduce it for security reasons, use a transformer. As it is a small electric motor is a transformer rather cheap.
These types of transformers can be used
**broken link removed**. You use only primary winding.
If it is a brush motor can a lamp dimmer be used to adjust torque, but back EMK can kill the dimmer. That is the reason for special motor-dimmers, which have some protection against back-EMK.