This is an old question but I thought it would be a good idea to remind people that if the adhesive tabs are broken, the safest thing to do is to remove the logic board before attempting to pry the battery out (heat or no heat). Remove the port & speaker too if you want lots of room to work from. That way you will minimize the deformation to the battery.
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The iPhone 5C has tiny surface mount components near the edge of the logic board near the battery connector. If you pry the battery from there, you can easily knock some components off the board. They are minuscule and once separated from the board, are indistinguishable from dust...seriously!