The ternary-arsenide compound BaCo2As2 was previously proposed to be in proximity to a quantum-critical point where long-range ferromagnetic (FM) order is suppressed by quantum fluctuations. Here we report the effect of Ir substitutions for Co on the magnetic and thermal properties of Ba (0 ≤ x ≤ 0.25) single crystals. These compositions all crystallize in an uncollapsed body-centered-tetragonal ThCr2Si2 structure with space group I4/mmm. Magnetic susceptibility measurements reveal clear signatures of short-range FM ordering for x ≥ 0.11 below a nearly composition-independent characteristic temperature Tcl ≈ 13 K. The small variation of Tcl with x, thermomagnetic irreversibility between zero-field-cooled and field-cooled magnetic susceptibility versus T, the occurrence of hysteresis in magnetization versus field isotherms at low field and temperature, and very small spontaneous and remanent magnetizations <0.01 μB/f.u. together indicate that the FM response arises from short-range FM ordering of FM spin clusters as previously inferred to occur in Ca(Co1−xIrx)2−yAs2. Heat-capacity Cp(T) data do not exhibit any clear feature around Tcl, consistent with the very small moments of the FM clusters. The Cp(T) in the paramagnetic temperature regime 25–300 K is well described by the sum of a Sommerfeld electronic contribution and Debye and Einstein lattice contributions where the latter lattice contribution suggests the presence of low-frequency optic modes associated with the heavy Ba atoms in the crystals.