In auto rotation the angle of attack is (on average, forget for a moment the asymmetries of rotating blades) such that blade drag (plus some remaining gearbox torque=drag) needs to be compensated at a given lift=weight.
For most heli's in auto rotation that maintain correct RPM (see earlier thread on danger of low RPM retreating blade stall with associated blow back in auto rotation) this average angle is well below the optimal angle of attack, optimal defined as giving best lift/drag ratio (geometrically defined by tangent to lift/drag curve) with other words the lift at the normal speed/drag is low.
Making the air thinner (smaller density) will increase this angle because to produce the same lift at lower density the angle must increase. This makes the rotor work more efficiently, so higher RPM is possible because more efficient lift/drag ratio.
Reverse could be true if the heli has highly loaded blades which is the case when heavy and RPM is kept too low, but this is not a design point
afaik.
The rigging specification takes TOW, DA, t° and humidity into account (everything influencing air density "ro").
It also needs COG because the body drag also influences the RPM, mostly more nose down will mean less body drag which means higher RPM.
Personally I use the memo technical aid "auto rpm does not like cold and dry" (=heavy air)
Hope that helps