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Servo motors will generally only get hot if the torque requirement is to high. Sizing a motor is a skill that is difficult to explain, however as a general rule the lower the torque the lower the current. Often a stalled servo within it's working current range will not over heat nor will it use much power, since the voltage is low across the motor but the current may be high the power used is low. Motors running near stall torque at full speed will use the maximum amount of power since the current is high and the voltage is also high, hence the heating effects on the motor will be at their maximum. Always try to mount motors with the largest possible metal contact area. Use a metal like aluminium that is a good conductor of heat to conduct the heat away from the motor and consider a fan if the duty cycle is high.


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