Is it permissible for me to live in my mother's house, which she bought with her own money, before her estate is distributed, on the condition that its ownership transfers to me after her death with the consent of the heirs, knowing that I am an heir and that the value of the house exceeds one-third [of her estate]?

If by dwelling in the house you merely mean residing in it, then there is no harm in your mother allowing you to live in the house she owns. This is not considered a gift or a bequest, and the house will be divided among the heirs after her death.

However, if you mean that she allows you to live in it during her lifetime and bequeaths the house to you after her death, then this is a bequest to an heir, which is not permissible in Islamic law unless the adult, sane heirs approve it. It then applies to the share of whoever approves it.

Furthermore, it is not permissible for her to gift you the house without giving her other children what would achieve justice in the giving, based on the Prophet's (peace be upon him) saying: "Fear Allah, and be just between your children."

Your need for housing can be met by providing accommodation without transferring ownership. Favoring you with a gift is not considered a way of addressing a need, because the need is met by enabling residence.