This doesn't sound like a suuuuper interesting application to be honest because there's already a way to do this directly, i.e. use chemically stored energy to

This doesn't sound like a suuuuper interesting application to be honest because there's already a way to do this directly, i.e. use chemically stored energy to keep stuff cool: phase change material (PCM) cool packs, especially when packaged into containers using vacuum insulated panels (VIPs, which achieve phenomenal U-values ). A PCM cool pack has a pretty constant temperature while absorbing heat and a VIP-clad container by itself has pretty phenomenal insulation already. There's no moving parts and no battery chemistry to degrade and no UNECE Dangerous Goods in these.