The remnant magnetism in the crust of Martian southern highland is associated with the magnetic sources at an average depth of ∼32 km. In this work, we investigate the magnetization of Martian crust via 1-D parameterized model for the stagnant-lid mantle convection. According to our model, the magnetization of Martian crust is likely to take place in the top-down manner during 4.1–3.7 Ga. To reproduce the average depth of magnetic sources below the southern highland, magnetite and Mg-ferrite are anticipated to be the magnetic carriers in the Martian crust, implying the serpentinisation therein. If magnetite is the only magnetic carrier in the Martian crust, the early climate must be warm enough to maintain a surface temperature of 300 K during 4.1–3.7 Ga at least. Such a warm climate is more likely to be a regional phenomenon associated with the serpentinisation in the crust of the southern highland or the hot ejecta of Borialis impact depositing on the southern hemisphere.