Laser-heated diamond anvil cell (LH-DAC) is needed to investigate melting properties of deep planetary interiors. Interpretation of the melting behavior is however challenging because extreme temperature gradients are inevitable. In this work, we investigate how the peak temperature at the center of the laser spot, from sample solidus to 1000 K above (Delta T), affects the chemical relations between melt and solid residue. We investigate the melting behavior of two possible mantle compositions, pyrolite and chondritic type material, at pressures corresponding to depths of similar to 1000 km and higher (40-73 GPa). Recovered samples are characterized at nanoscale spatial resolution using electron microscopy. Samples tend to show that chemical composition of melts and bridgmanite-melt relations vary largely with peak temperature. With increasing Delta T, the (Mg,Fe) exchange coefficient (K-Fe-Mg(Bg/melt)) decreases from 0.29 to 0.11, and SiO2 contents in melt ([SiO2](melt)) from 43 to 18 wt%. In addition, we observe that the higher Delta T, the more the liquid is depleted in bridgmanitic-type composition. These experimental features are contrary with those expected from the known melting diagram of typical mantle material. Instead, they are well explained by considering fast solidification of bridgmanite (Bg) at the edge of the molten zone, in disequilibrium conditions. The sample prepared at solidus temperature and for short duration presents a central melt pool of Ca-bearing melt in close contact with Bg and ferropericlase. The degree of partial melting is coherently estimated to 18(2) wt% by two independent observations. This corresponds to pseudo-eutectic conditions where only the third mineral, davemaoite, is exhausted. For a pressure of 40.5 GPa, K-Fe-Mg(Bg/melt) and [SiO2](melt) are found to be 0.29 and 43 wt%, respectively, in good agreement with multi-anvil press experiments. Altogether, this work shows that erroneous solid-liquid chemical relations can arise from samples synthesized at temperatures well above solidus in the LH-DAC.