Taking the problem step-by-step, the temperature rise of the motor will depend on the losses and the cooling.
Looking at the losses first, and putting aside the effect of the inverter harmonics for a moment, a reasonably well balanced design of induction motor may have rated condition losses in the very approximate proportions 25% stator copper loss, 15% rotor copper loss, 40% stator core loss, 20% friction and windage loss (and I've neglected stray loss). These figures will vary according to the motor rating, and I don't have access to design calculations covering 5hp, but they will do for this. Your machine will have a total loss of about 470W at the rated condition, based on stated 87.5% efficiency.
Running at 1/10th speed will dramatically reduce the iron loss, which is proportional to something between speed and speed squared. The stator copper loss will also reduce; at .3hp torque will be about 60% of full load torque and assuming current reduces in roughly the same proportion, the stator copper loss will be less that 40% of the full load value. This is approximate, the equivalent circuit of the induction motor has the magnetizing current branch across the motor terminals but as the voltage is reduced (in proportion with the speed) the magnetizing current will be drastically reduced compared with the torque producing component.
Friction and windage is also going to fall fairly dramatically though this loss will not tend to affect the winding temperature. At rated speed most of the f&w loss probably comes from the fan.
So for sine wave operation, your losses will fall to something under 100W, say 20% of full load losses. Although the fan air volume will be 10% of that at the rated speed, the motor will be able to dissipate far more than 10% of the full load losses. For example, see fig.5 in radarrays link - assuming the speed axis goes down to zero, this shows that at zero speed the 180T motor can still operate at about half power (the curve is for TEFC motors but I don't think this matters).
Even with no forced air movement, a 184T frame has enough dissipative surface to shift about 125W with a 60degC temperature rise, based on 12W/m^2 degC in metric units.
So I don't think there will be a problem, even with some loss added due to inverter harmonics. If anything is going to suffer it will be the winding, so if it's accessible you could always put a thermocouple on the end-winding to check.