We define a value-based modal µ-calculus, built from firstorder formulas, modalities, and fixed point operators parameterized by data variables, which allows to express temporal properties involving data. We interpret this logic over µCrl terms defined by linear process equations. The satisfaction of a temporal formula by a µCrl term is translated to the satisfaction of a first-order formula containing parameterized fixed point operators. We provide proof rules for these fixed point operators and show their applicability on various examples.