We study magnetism in magnetically doped quantum dots as a function of confining potential, particle numbers, temperature, and strength of Coulomb interactions. We explore possibility of tailoring magnetism by controlling the electron-electron Coulomb interaction, without changing the number of particles. The interplay of strong Coulomb interactions and quantum confinement leads to enhanced inhomogeneous magnetization which persist at higher temperatures than in the noninteracting case. The temperature of the onset of magnetization can be controlled by changing the number of particles as well as by modifying the quantum confinement and the strength of Coulomb interactions. We predict a series of electronic spin transitions which arise from the competition between the many-body gap and magnetic thermal fluctuations.PACS numbers: 75.75.+a,75.50.Pp, Magnetic doping of semiconductor quantum dots (QDs) provides an interesting interplay of interaction effects in confined geometries [1,2,3,4,5,6,7,8] and potential spintronic applications [9]. In the bulk-like dilute magnetic semiconductors the carrier-mediated ferromagnetism can be photoinduced [10,11] and electrically controlled by gate electrodes [12], suggesting possible nonvolatile devices with tunable optical, electrical, and magnetic properties [9]. QDs allow for a versatile control of the number of carriers, spin, and the effects of quantum confinement which could lead to improved optical, transport, and magnetic properties as compared to their bulk counterparts [1,13,14]. Unlike in the bulk structures, adding a single carrier in a magnetic QD can have important ramifications. An extra carrier can both strongly change the total carrier spin and the temperature of the onset of magnetization which we show can be further controlled by modifying the quantum confinement and the strength of Coulomb interactions.We study the magnetic ordering of carrier spin and magnetic impurities in (II,Mn)VI QDs identified as a versatile system to demonstrate interplay of quantum confinement and magnetism [4,5,6,15,16,17,18]. Because Mn is isoelectronic with group-II elements it does not change the number of carriers which in QDs are controlled by either chemical doping or by external electrostatic potential applied to the metallic gates. The latter allows confinement of the carriers in a dot with tunable size and shape [2]. By using real space finite-temperature local spin density approximation (LSDA) [19] we study temperature (T ) evolution of magnetic properties of QDs over a large parameter space. This approach allow us to consider QDs with varying number of interacting electrons (N ) and Mn impurities (N m ) which already for small N and N m becomes computationally inaccessible to the exact diagonalization techniques [18,20]. We extend the previous studies of Coulomb interactions in magnetic QDs with N m = 1, 2 at T = 0 [18] and T > 0 results using either Thomas-Fermi approximation or by applying Hund's rule with up to 6 carriers [17]. We reveal that the interplay of strong Cou...