A cage for withholding rolling bodies in a rolling bearing, comprising a single annular body provided with a plurality of seats or pockets arranged as a crown, each delimiting a respective radially through alveolus, each one being adapted to house a respective rolling body, withholding it at least radially outwards, by means of a first edge of a first annular portion of the body, arranged radially on the outside of the body, and, optionally, also radially inwards by means of a second edge of a second annular portion of the body, arranged radially on the inside of the body; wherein, in combination: i) the body is made of a material having a thermal expansion coefficient greater than that of the materials of which the rolling bodies and an outer ring of the rolling bearing, which the cage is intended for, are made; ii) at ambient temperature, the first edge guides the rolling bodies resting thereon, directly cooperating therewith with a set first radial clearance; iii) in use, at the working temperature of the bearing and above a set speed threshold, the first edge no longer guides the rolling bodies, leaving them free to roll substantially without friction with the cage, due to a set increase in the value of the first clearance, while a radially outer cylindrical lateral surface of the first annular portion of the body cooperates with a second radial clearance, under such conditions smaller than the first one, with the outer ring of the bearing; characterized in that: iv) the cage is dimensioned so that a pitch diameter (Dpc) of a crown of rolling bodies housed in use in the crown of seats or pockets of the cage is greater than a pitch diameter (Dpa) of the crown of alveoli delimited by the seats or pockets, so that there is an eccentricity (e) between the geometric centers of the alveoli and the geometric centers of the rolling bodies for each alveolus in use; and in that v) radially outwards and at the respective alveolus, each seat or pocket has a radially through cylindrical portion or cavity radially aligned with the alveolus underneath, having a diameter smaller than a transversal dimension of the rolling bodies. i) the body is made of a material having a thermal expansion coefficient greater than that of the materials of which the rolling bodies and an outer ring of the rolling bearing, which the cage is intended for, are made; ii) at ambient temperature, the first edge guides the rolling bodies resting thereon, directly cooperating therewith with a set first radial clearance; iii) in use, at the working temperature of the bearing and above a set speed threshold, the first edge no longer guides the rolling bodies, leaving them free to roll substantially without friction with the cage, due to a set increase in the value of the first clearance, while a radially outer cylindrical lateral surface of the first annular portion of the body cooperates with a second radial clearance, under such conditions smaller than the first one, with the outer ring of the bearing; characterized in that: iv) the cage is dimensioned so that a pitch diameter (Dpc) of a crown of rolling bodies housed in use in the crown of seats or pockets of the cage is greater than a pitch diameter (Dpa) of the crown of alveoli delimited by the seats or pockets, so that there is an eccentricity (e) between the geometric centers of the alveoli and the geometric centers of the rolling bodies for each alveolus in use; and in that v) radially outwards and at the respective alveolus, each seat or pocket has a radially through cylindrical portion or cavity radially aligned with the alveolus underneath, having a diameter smaller than a transversal dimension of the rolling bodies.