Austerity in itself is not a limb of bhakti. Bhakti has sixty-four limbs; this means that there are sixty-four types of activities which give us bhakti but austerity is not amongst them.
However, austerity is glorified in the scripture that by performing sacrifice, by giving in charity and by engaging in austerity even saintly men are being purified. So in this sense, austerity is held in high esteem in the scripture. It is also said, nayam deho deha-bhajam nrloke, kastan kaman arhate vid-bhuja