If an inducation motor is run with lower voltage, more current will be drawn and more heating will occur.  The NEMA MG-1 limit for voltage at the terminals of the motor is within 10% of rated (nameplate) voltage (assuming frequency does not deviate from rated).  Therefore 203.4 would be minimum allowed voltage.  Note this should be measured at motor terminals (or if measured remotely you should allow for voltage drop in the cable).

In general I don't believe there is any "magic" associated with that threshhold.  The heating will increase with decreased voltage... but heating is also affected by mechanical load (temperature of the pool), ambient temperature (assumed 104F ambient... you are probably less) etc.

Also voltage generally should not drop below 80% during starting of the motor (otherwise the motor may stall or overheat while starting).

Two additional points -
1. By increasing the fan speed, you have increased the load.  I believe that this is a cube law, so that by doubling the speed you have increased the load by a factor of (2^3) = 8 (please check the specifics, I am dredging this out of memory).  If this is the case, you would probably have burnt the motor due to overloading, compounded by the low voltage factor that electricpete discusses above.
2. Related to the above, what overload protection was provided for the motor?  This should be sized correctly to prevent motor burnout due to excess load current.

Once again electricpete and peterb nailed this one down. Stars for pete and pete...

how the drop in voltage causes motor heat

The motor is almost a constant-speed device.  That means that when you couple it up to a given mechanical load (fan), it will draw almost a constant power, regardless of voltage change.

IF for simplicity, we assume that the power factor is constant, then the power is proportional to voltage times current  (P ~ V*I).  From this it is easy to see that if power is to be constant, current must increase when voltage decreases.

Regarding our assumption of constant power factor, it was not 100% correct.  Actually a decreasing voltage generally means an increasing power factor, which would tend to decrease current!... but this effect is usually much less than the primary effect causing current increase identified above.

Suggestion: Often, it is a combination of adverse conditions, e.g.
1. Higher RPMs
2. Higher current
3. Not sensitive protection
4. Lower motor terminal voltage than the NEMA MG-1 allows (10%)
5. Etc., maybe: motor design letter, NEMA Code Letter (LRA), Insulation Class Level low, power quality low (high harmonic content),....