Bob Shuman wrote:
...... the piece I missed in the spec
sheet is the maximum 3A in rush current. Where was this specified?

http://www.skceramic.com/pro-ntc_power_kr.htm
Column labeled 'at 25ºC (A)' - 3A
25ºC is the starting temperature and thus the 3A must be the inrush
current, or at least this is the way I read it.

I think you've hit upon why the part exploded and burned up. It
appears it was indeed undersized for the application. So from their
listing, which part has the higher in rush current limit? Again, I
did not see this specified in the part list table. Thanks in advance.

I would replace it with a NTC 5D-18 which has a 7A current rating.