Intermittent power dissipation calculation on TO-220 package
The question is: is a heatsink necessary for a 60 second (max)
  operating time?


Wikipedia says: -


  When a TO-220 package is used without a heatsink, the package acts as
  its own heatsink, and the heatsink-to-ambient thermal resistance in
  air for a TO-220 package is approximately 70 °C/W.


This means that without an external heatsink, the T0-220 heatsink will rise 70 °C for each watt dissipated.


  Can I get away with a large enough copper plane?


I'm sure you can but you are going to have to do some thermal analysis.