Carrot (Daucus carota L.) is a globally consumed root vegetable, enjoyed both raw and after thermal processing. This study aimed to evaluate the effect of different heat treatment methods (traditional boiling in water, steaming in a steel pot, steaming in a combi oven, baking in a combi oven, and the sous-vide technique) on carrot color, total phenolic and flavonoid content, phenolic and carotenoid compound profiles, and antioxidant capacity. It was found that heat treatments resulted in significant (p ≤ 0.05) changes in carrot color, with reductions in lightness (L* decreased by 19–24%), redness (a* decreased by 52–67%), and yellowness (b* decreased by 15–25%). Interestingly, processed carrots showed an increase in total phenolics (by 25–133%), total flavonoids (by 60–126%), and total carotenoids levels (by 16–48%) compared to raw carrots. However, specific phenolic and carotenoid compounds showed notable reductions (p ≤ 0.05) after heat treatment, including vanillic acid and rutin (100% reduction after all treatments), α-carotene (up to 33.3% reduction after baking), zeaxanthin (up to 33.3% reduction after baking), and 13-cis-β-carotene (up to 40.7% reduction after steaming in a combi oven). In addition, heat treatment significantly (p ≤ 0.05) increased the antioxidant capacity of carrots, as determined by DPPH and ABTS assays, with increases up to 2.2-fold and 1.6-fold, respectively. The antioxidant properties of processed carrots were strongly correlated (p ≤ 0.05) with total phenolic content and the levels of chlorogenic acid, p-coumaric acid, and β-carotene (r = 0.86–0.96).