Motivation: The "New Worlds, New Horizons", 2010 Astronomy Decadal Survey stated that the pursue of phased array technologies to gain full access of the instantaneous field of view (FOV) of a telescope optics, will enable gains in mapping speed of orders of magnitude in current and future radio telescopes. To realize this goal, we have developed a fully cryogenically cooled 19-element, dual polarized, phased array prototype camera for the Arecibo radio telescope that works at L-Band (1.2 to 1.7 GHz). One key aspect of the design is a 70cm diameter vacuum window consisting of a Kapton membrane supported by radio-transparent foam capable of withstanding loads in excess of 200 psi. In order to support the ~5 tons of atmospheric pressure on the window, without having unreasonably high thermal loads, a detailed structural and thermal analysis and simulation was performed, resulting in a trade-off between structural and thermal loads in the cryostat design.