General Circulation Models (GCMs) exhibit systematic biases that limit their direct applicability. Bias correction (BC) techniques aim to reduce these errors by adjusting GCM outputs to better match observed climate statistics. This study evaluates the performance of the MVT (Mean and Variance with non-linear Trend) bias correction method, which adjusts the climatological mean, inter-annual variance, and used multi-model ensemble (MME) non-linear trend of GCM temperature data. The CESM2 model was selected under historical experiment of 1976-2014 and SSP585 and SSP126 scenarios during 2027–2056 over south of Iran (including Sistan-va-Baluchestan, Kerman, Fars, Bushehr and Hormozgan). The goal is to assess the magnitude, seasonality, and stability of the corrections using ERA5 reanalysis. The MME non-linear trend derived from 19 CMIP6-GCMs replacing the original non-linear trend of CESM2. Then the values of CESM2-BC - CESM2 were analyzed in historical period, based on ERA5 data. Results showed that the raw model exhibits a systematic temperature-dependent bias across different seasons. Following, temperature projection under the two scenarios was focused. To this aim monthly temperature and trends of CESM2-BC - CESM2, and P5, P25, P50, P75, P95 percentiles of temperature distribution from CESM2-BC and CESM2 were analyzed. Results indicated that the effect of bias correction varies strongly by season. Under SSP585, CESM2-BC produces underestimates (negative differences) during the cool months (October–April) and overestimates (positive differences) during the warm months (May–September). The total underestimation from October to April amounts to –8.3°C, while the total overestimation from May to September reaches +7.0°C. Switching to SSP126 preserves the same seasonal sign: cool-month underestimation totals –6.3°C, warm-month overestimation totals +11.0°C. The largest monthly underestimation occurs in December for both scenarios (–2.4°C under SSP585 and –1.9°C under SSP126). The month of maximum overestimation shifts from June under SSP585 (+2.5°C) to July under SSP126 (+2.8°C). Over the 30-year period, the difference between CESM2 and CESM2-BC shows distinct trends depending on the month and scenario. Under SSP585, most months exhibit a positive trend (i.e., the correction becomes larger over time), except August where the slope is near zero. The steepest positive slopes occur in May (1.3°C/decade), November (0.68), December (0.65), and January (0.57). This indicates that under strong radiative forcing, the bias correction is non stationary and amplifies with warming. In contrast, under SSP126 the trends are generally milder; the largest positive slopes are still in cool months (November 0.59°C/decade, February 0.57), but March displays a negative slope (–0.22), suggesting potential over correction in late winter. From July to October, SSP126 yields larger positive slopes than SSP585, implying a stronger time dependence of the correction under the low emission scenario during those months. To disentangle whether the observed differences arise from a shift of the entire distribution or from changes in the tails, the percentiles were examined. Under SSP585, the median varies between –1.0 and +0.5°C across months, indicating only a modest shift of the central tendency. However, the cold tail is strongly negative in all months, reaching –4.0°C in December. The warm tail is positive in spring and summer but occasionally negative in autumn. The both P95 and P5 deviate substantially from the median, demonstrating that the correction primarily affects the extremes rather than the bulk of the distribution. Under SSP126, P5 and P25 are consistently and strongly negative across all months, while P50 remains near zero or slightly negative. P95 is positive in many months but can also be negative, showing less systematic behavior. These patterns indicate that the MVT correction systematically reduces the bias of the raw CESM2 model by straightening and reordering the disordered percentile structure. Crucially, the correction is quantile- and season-dependent, achieving its most pronounced in the warm tail, especially during the first half of the year. In contrast, the cold tail experiences more limited modifications. Thus, the correction does not simply shift the mean but dynamically reshapes the distribution, focusing heavily on correcting the warm extreme underestimations. The performance and stability of MVT are strongly scenario dependent. Under the SSP585, the correction exhibits a pronounced time dependence, with positive trends in most months and larger magnitudes in the cold season. Under the SSP126, the correction is more stationary and therefore more reliable for long term applications. The physical expectation that the weaker forcing leads to less deviation from the calibration period is confirmed. Overall, in spite of MVT bias correction valuable improvements for temperature projection in the studied area, but its application must consider the scenario dependent stability. Future work should extend this evaluation to other variables and regions to further assess the robustness of MVT.