How can I create a movable insulated wall?
Because your temp differential is relatively high (72˚F vs 35˚F), and you're talking about a relatively large area (I assume, because you talk about accordion "walls"), unless you have a fairly powerful air conditioner or very good wall insulation, your cooling requirements will be challenging.

If it's important that the wall be an accordion wall, then I would think in terms of 2 or 3" thick rigid foam polystyrene wall panels, with edges framed by ¾"x 2(or3)" plywood, with alternating-side hinges linking the individual panels to achieve the accordion effect.