Insulating the table bottom and sides, according to your unstated climate needs, and putting and insulating cover over it might work, again, not knowing your climate. Mass would help in winter, like filling in the sides of the base, moving the insulation down to the earth, and filling in the space below the bed with water containers.
Orienting E-W by length, and replacing the north roof panel with a white insulating panel would help with winter also. Burying some self regulating heat tape under some sheet metal under your bed might also be helpful...it could be on a thermostat for very cold nights.
Heat build up, even in winter on sunny days is also a serious issues for such a cold frame - like design. Automated panel openers- even the wax cylinder type could be plant heroes. I used a frame like this as a season extender for years.
