On some remod jobs they build out with 2X6 around the load center opening, and then insulate before setting the panel, with an existing panel there is usually no space to insulate, some remod jobs they build out the entire area and add an insulation with a super rating to conserve on energy.
You could slip sheets of the thin styrofoam one at a time behind the panel. You may also want to try that foil backed bubble wrap stuff (excuse my technical lingo). No one else said it, but I bet they are thinking it, so I'll be the first to say it, spray foam.
This thread got me wondering where the heat that may build inside the panel is supposed to dissipate? If the recessed panel is well insulated all around and behind, then it's through the front cover?
Would there really be enough heat to even worry about it? I guess it depends on the loads and connections.