To realize the quantum anomalous Hall effect (QAHE) at elevated temperatures, we adopted the approach of magnetic proximity effect (MPE) to break time reversal symmetry in topological insulator (Bi,Sb)2Te3 (BST) based heterostructure with a ferromagnetic insulator like europium iron garnet (EuIG) of perpendicular magnetic anisotropy. Here we demonstrated phenomenally large anomalous Hall resistance (RAHE) as high as 8 {Omega} at 300 K, and sustained to 400 K in 35 BST/EuIG samples, surpassing the past record (0.28 {Omega}) by nearly thirty times. These striking results are attributed to an atomically abrupt interface between BST and EuIG being Fe rich. Importantly, the gate dependence of AHE loop showed no sign change with varying chemical potential, thus the MPE induced AHE is less likely originated from the extrinsic effect. For gate-biased 4 nm BST on EuIG, pronounced topological Hall effect coexisting with AHE were observed at the negative top gate voltage up to 15 K.
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