Bias correction of climate model temperature fields in the image domain is difficult because general circulation model (GCM) outputs and observation-based references occupy different statistical distributions at each grid cell, so pixel-wise regression can recover spatial structure while leaving distributional biases intact. This study presents a two-stage Transformer framework, bias-corrected high-resolution restoration (BHRR), that addresses this problem by decoupling spatial restoration from distribution-aware bias correction. The framework is evaluated on daily near-surface temperature fields over a fixed 200×280 grid-point (latitude × longitude at 0.25° resolution) Oceania domain by sequentially coupling spatial restoration and distribution-aware bias correction. In the first stage, a Restormer model restores high-resolution spatial structure from linearly interpolated model fields. In the second stage, a Vision Transformer predicts a reference-based quantile map that is used as an explicit transfer function for equidistant cumulative distribution function (CDF) matching in future projections. Across daily minimum, mean, and maximum near-surface air temperature, the restoration stage improves spatial fidelity, increasing median structural similarity to 0.876–0.908 and median peak signal-to-noise ratio to 26.6–28.1 dB. The bias-correction stage further reduces systematic error, yielding near-zero median percent bias (<0.1%) and lowering median root mean square error (mean temperature by approximately 0.5 K and maximum temperature from 4.4 K to 3.7 K). To verify that the framework preserves climate-change signals rather than collapsing future projections toward historical climatology, future projections under SSP2-4.5 and SSP5-8.5 are examined using ETCCDI extreme indices and Sen's slope. The results confirm scenario-dependent differences in extreme-temperature diagnostics, and spatial-variability analysis shows patterns consistent with a standard downscaled benchmark, supporting the use of the BHRR v1.0 framework as a technical post-processing tool for distribution-aware bias correction of gridded climate fields.