They don’t need heat to gain energy from it. They need heat to survive the massively endothermic process of laying down their energy stores.
The Grokes evolved in a high temperature environment where food occasionally showed up in large quantities and was scarce the rest of the time. As a response they evolved a highly sophisticated, highly efficient, highly energy dense ‘fat’ analogue that uses a series of catalyst enabled endothermic reactions to ‘lock in’ as much of that energy as possible to save for later.
In their natural habitat these reactions aren’t an issue. The Groke would simply be quite cool just after feeding.
Here, however, it’s too cool. A freshly fed Groke needs to find a good heat source to keep itself warm while it’s body lays down it’s ‘fat’ stores. This means Grokes hunt not only for food, but for food and heat.
Now a sensible Groke will regulate its food intake, eating little and often and simply presenting as a cool bed sheet ghost rather than a freezing funereal shroud of death. Even more sensible Grokes have handy heat sources nearby and do their best not to kill them, as only a fool kills a still warm moomin.
Of course, once a Groke has fed it can go for a long, long time (at a more reasonable temperature) without needing extra food, or burn up those energy stores incredibly quickly (and hotly) by reversing the process. They can also survive up to quite extreme heats (which remind them of home).