At least would stay on but needs at least 3x dissipation area than that support chip sink has. In free air I'd start with a guess of 5 sq. inches of surface PER-CHIP.
5 square inches? The problem is that there are capacitors in the way of the chip, so you can't mount a big one.
Here is photo:

See the four orange capacitors that's in the way of mounting a sufficiently large heat sink? Anyway around this?