What would cause my eReader's battery to suddenly start smoking?
It is likely but not certain that the battery was AND IS faulty and that you risk destruction of you eReader if you continue to use this battery. LiIon (Lithium Ion) batteries have a mode euphemistically known as "vent with flame" - which well enough describes the failure mode. Usually such events destroy the battery, and often also the device they are used in. It is possible that your battery had a marginal failure that discharged it at a high rate but did not 'quite' cause destruction. 

A less likely reason is a fault in the battery connection system. A look at the "insert battery" section of the manual indicates that this is possible but highly unlikely.

The next most likely reason is that there is a fault in the reader which caused a temporary short circuit of the battery. If so, the short may have been destroyed by the incident but this can not be depended on. If it happens again the device could be destroyed.

Regardless of the reason for the failure, it represents a manufacturing or design fault in the system and a reputable manufacturer should at a minimum replace the battery at no cost, and the e-Reader if there is any suspicion whatsoever that it is the cause of the problem. Manufacturers such as Apple have replaced many millions of dollars of just-maybe-faulty product on the basis of a fraction of a percent of overall failures.   

The only exception to the above is if you have charged the battery with a non-standard charger. LiIon batteries can be damaged by the use of incorrect charging methods and (less likely) by unmatched LiIon chargers.