... I was just worried that it was running hotter than it really should given its current draw. ...
How do you know if this is the case? Did you measure the case temperature when the same pump is running Across-The-Line to compare? 160F is not that unusual for a fully loaded motor.
Besides, contrary to popular belief, case temperature means nothing in a motor, unless you are tracking it and you see a CHANGE. If you have RTDs embedded in the WINDINGS, that's meaningful information, but the outside case temperature varies by design, cooling fins, air flow, air gap, etc. etc. Bottom line, there are no generalizations you can make.
Measure the current, or in this case, read it from the VFD display. As long as you are within the FLA rating of the motor, you are fine. Now, one thing that IS true is that running a motor from an inverter DOES increase the heating in the motor slightly. For this reason, 99% of motor mfrs will tell you that if you have a motor with a Service Factor (i.e. 1.15 or 1.25 in your case), the SF is consumed in the harmonic heating effect, so you should ALWAYS treat any motor run from an inverter as having a 1.0SF. Conversely, you should NOT use a motor that is rated for 1.0FS on an inverter drive unless the motor mfr. explicitly says that you can (and backs that up with a warranty).
Now, separate issue:
Being that this motor only has Class B insulation, I'd hazard a guess that this is NOT an "inverter duty" motor. For THAT reason, I would put a dv/dt filter on the output of the drive. Forget heating, there are other more real and damaging issues with running off-the-shelf general purpose motors from a VFD, many of which can be attenuated by using a dv/dt filter, or if there is over 3,000ft from the VFD to the motor, a Sine Wave filter.