There are many aspects in which the sacrificial service in the Temple in Jerusalem is stricter than that of the private altar. However, there are three aspect in which they are the same.
One is liable for the following on a private altar: if he eats the sacrifice beyond the allowed time; if one had a wrong intent to eat the sacrifice beyond allowed time, the sacrifice becomes invalid and one is liable for eating it; one is liable for eating it while being ritually impure.
How do we know that? In fact, we might even think the opposite. The Torah stated that a sacrifice kept overnight is burned and one that goes out of the Temple is also burned. Therefore I might think that since the sacrifice on the private altar already exited the Temple and was not burned, so too one that was left overnight is not burned! - Bird sacrifices disprove this, since they are less strict than the animal sacrifices, and they do become invalid with time. - Birds are no proof, because they require a kohen. To dispel all these arguments, the Torah said, “This is the law of the peace offerings” - to be applied both inside and outside the Temple.
Art: Frans Snyders - Concert of Birds