Yeah, happy grubs don't move much. If they like their food they are very content to just stay parked in a spot until they're surrounded by poop. Their poop looks rectangular and being able to identify it among your compost is a good skill to have. I was worried about mine at first, but that just meant they were very happy with their food. My ox beetles used to churn around a lot until I figured out their "ratio" of leaf and stuff they like and now I rarely see them move save for when they're scooping up food against the very side of their jars.
I only check my grubs once a month and that's only if I absolutely need to and I keep dates for every change of their food/soil so I know about how much they have gone through without actually digging them up to check the poop quantity. Sticky notes are good for this.
I would only worry if they were at the top of the soil crawling around. If they're up on top of the soil, chances are something is wrong but not always, as sometimes they do that if they're totally out of food and they're looking for something good to eat. Or it could be mites, or an injury, or they don't like the soil they're in to pupate because they can't compact it. Then they waste a lot of energy and may not pupate properly. Unless your grub is very large, I don't think you need to worry about pupas right now.
So if you're grubs aren't moving much, you're probably doing great is what I'm saying. Cold temperatures will also make them sluggish but it shouldn't hurt it unless it's at freezing in your house.
Also, if you're giving it wood chunks, you might want to bake the wood at a low temperature, or pour boiling water on it to kill mites and predators in it, such as wire worms. It's not required, but heavy mite infestations are awful and certain kinds of mites can hurt your grub(s). Wire worms can kill pupa.
Sorry, that was a lot.