Method for regulating at least one of the parameters (a) of a method for the hot-rolling of a part-finished metallic product through at least one stand of rolls of a rolling mill comprising at least two working rolls, the regulating method comprising the following steps of calculating a forward slippage ratio (FWS) using the following equation: FWS = (a) where vout is the speed of the part-finished product leaving said stand and νstand is the linear speed of the working rolls; calculating an estimate of a coefficient of friction (μactual) as a function of a measured value of the clamping force (F) of said working rolls in the stand and of the forward slippage ratio (FWS) previously calculated; and regulating at least one of the parameters (a) on the basis of the calculated estimate of the co-efficient of friction (μactual). Associated rolling method, associated rolling mill and associated computer program product.