Corn or baby corn is not chilling sensitive and should be kept as close as possible to 0°C.  Regarding MAP, oxygen concentrations in the range of 3-5% and carbon dioxide in range of 5-10% are conditions that are usually reported as beneficial to quality and shelf-life.  Below are some references on corn.  I doubt that conditions for baby corn would differ. 

• Aharoni, Y., Z. Copel, M. Gil and E. Fallik.  1996.  Polyolefin stretch films maintaining the quality of sweet corn during storage and shelf-life.  Postharvest Biol. Tech. 7: 171-176.
• Brecht, J.K. 1998.  Fresh-cut sweet corn kernels.  Citrus and Vegetable Magazine 63(7): 36-37.
• Deak, T., E.K. Heaton, Y.C. Hung and L.R. Beauchat.  1987.  Extending the shelf life of fresh sweet corn by shrink-wrapping, refrigeration, and irradiation.  J. Food Sci. 52(6): 1625-1631.
• Manleitner, S., F. Lippert and G. Noga. 2003. Post-harvest carbohydrate change of sweet corn depending on film wrapping material. Acta Hort. 600: 603-605.
• Morales, Castro, J.,  M.A. Rao, J.H. Hotchkiss, and D.L. Downing.  1994.  Modified atmosphere packaging of sweet corn on cob.  J. Food Proc. Preserv. 18: 279-293.
• Riad, G.S., J.K. Brecht and S.T. Talcott. 2003. Browning of fresh-cut sweet corn kernels after cooking is prevented by controlled atmosphere storage.  Acta Hort. 628: 387-394.
• Risse, L.A. and R.E. McDonald. 1990.  Quality of supersweet corn film-overwrapped in trays.  HortScience 25(3): 322-324.
• Rodov, V., A. Copel, M. Aharoni, Y. Aharoni, A. Wiseblum, B. Horev, and Y. Vinokur. 2000.  Nested modified-atmosphere packages maintain quality of trimmed sweet corn during cold storage and the shelf life period.  Postharvest Biol. Tech. 18: 259-266.

I hope this is helpful. –