We use inelastic neutron scattering to study temperature dependence of the paramagnetic spin excitations in iron pnictide BaFe2As2 throughout the Brillouin zone. In contrast to a conventional local moment Heisenberg system, where paramagnetic spin excitations are expected to have a Lorentzian function centered at zero energy transfer, the high-energy (hω > 100 meV) paramagnetic spin excitations in BaFe2As2 exhibit spin-wave-like features up to at least 290 K (T = 2.1TN ). Furthermore, we find that the sizes of the fluctuating magnetic moments m 2 ≈ 3.6 µ 2 B per Fe are essentially temperature independent from the AF ordered state at 0.05TN to 2.1TN , which differs considerably from the temperature dependent fluctuating moment observed in the iron chalcogenide Fe1.1Te [I. A. Zaliznyak et al., Phys. Rev. Lett. 107, 216403 (2011).]. These results suggest unconventional magnetism and strong electron correlation effects in BaFe2As2. The elementary magnetic excitations (spin waves and paramagnetic spin excitations) in a ferromagnet or an antiferromagnet can provide direct information about the itinerancy of the unpaired electrons contributing to the ordered moment. In a local moment system, spin waves are usually well-defined throughout the Brillouin zone and can be accurately described by a Heisenberg Hamiltonian in the magnetically ordered state. The total moment sum rule requires that the dynamical structure factor S(q, ω), when integrated over all wave vectors (q) and energies (E =hω), is a temperature independent constant and equals to m 2 = (gµ B ) 2 S(S + 1), where g is the Landé g factor (≈ 2) and S is the spin of the system [1]. Upon increasing temperature to the paramagnetic state, spin excitations in the low-q limit can be described by a simple Lorentzian scattering function, where κ 1 is the temperature dependent inverse spin-spin correlation length and Γ is the wave vector dependent characteristic energy scale [2][3][4]. At sufficiently high temperatures above the magnetic order, spin excitations should be purely paramagnetic with no spin-wave-like correlations. Therefore, a careful investigation of the wave vector and energy dependence of spin excitations across the magnetic ordering temperature can provide important information concerning the nature of the magnetic order and spin-spin correlations. For example, a recent inelastic neutron scattering study of spin excitations in one of the parent compounds of iron-based superconductors, the iron chalcogenide Fe 1.1 Te which has a bicollinear antiferromagnetic (AF) structure and Néel temperature of T N = 67 K [5][6][7][8][9][10][11], reveals that the effective spin per Fe changes from S ≈ 1 in the AF state to S ≈ 3/2 in the paramagnetic state, thus providing evidence that Fe 1.1 Te is not a conventional Heisenberg antiferromagnet but a nontrivial local moment system coupled with itinerant electrons [12].Since antiferromagnetism may be responsible for electron pairing and superconductivity in iron-based superconductors [13,14], it is important to determine...