The deal comes two days after the Panthers got Jaromir Jagr from New Jersey for a pair of draft picks.
Fleischmann had 27 goals for Florida three seasons ago, and 27 goals in 180 games since. Fleischmann had seven goals and 14 assists for the Panthers this season.
Heatley was scoreless in six games with Anaheim, and hasn't been in the NHL since December. The former rookie of the year has a pair of 50-goal seasons and has 791 points in 869 career regular-season games.
The Panthers announced the trade about an hour before their game against Buffalo on Saturday.
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