The old problem of erosion by temperate glaciers is reviewed. We restrict ourselves to a monolithologic erosion of hard beds where chemical weathering is almost negligible. Rock fracture, either subglacial or otherwise, may have occurred during a previous cold episode, allowing long-lasting quarrying by the temperate glacier, but, once all the loosened material had been dragged away, grooving becomes the main erosional process. The theory of locally stress-controlled temperatures leads to the idea that very small particles found in the bottom ice cannot reach the bed. Therefore, abrasion and polishing come from rock chips due to grooving or sand grains freed by suglacial chemical weathering. In the steady regime, clasts that are able to groove come from the surrounding rock walls. Most of them do not enter the bergschrund, but are embedded in a bottom layer, which melts progressively over several kilometres. After being in contact with the bed over some distance, they are sufficiently blunted to become unable to groove. This distance. λ, increases with the boulder size, and the largest ones are not yet worn out at the glacier terminus. The mechanics of grooving is roughly modelled to estimate, for any stone size, the grooved volume per unit time and the grooving distance λ. From these estimations, and the size distribution, the erosion rate without quarrying as a function of the distance from the head wall, is calculated. It goes through a maximum when all the debris-laden bottom layer has just melted, and thus an overdeepening might form in a steady way. However, two unknown parameters enter the theory the probability ∏ for a stone able to groove which is in contact with the bed to groove and the ratio k of the volume of grooved rock before the stone is worn out to the volume of the stone. Experiments that may allow us to determine them are indicated below.