What is the Theta JC value for the BG388 package? This is not listed in the table on the Device Package User Guide, at: http://www.xilinx.com/bvdocs/userguides/ug112.pdf.
The BG388 package is a System ACE MPM (multi-package module). It does not need a heat sink because the System ACE device works only during configuration of Xilinx FPGAs on the board. If a heat sink is not required, Theta JC is usually not necessary. The package comes with a protective metal cap or lid which should help in heat dissipation.
Theta JA is what we specify for this package, which is 34.7 deg C/W.