In a previous work, we observed that heat-stressed goats suffer reductions in milk yield and its contents of fat and protein. Supplementation with soybean oil (SBO) may be a useful strategy to enhance milk quality. In total, eight multiparous Murciano–Granadina dairy goats (42.8 ± 1.3 kg body weight; 99 ± 1 days of lactation) were used in a replicated 4 × 4 Latin square design with four periods; 21 d each (14 d adaptation, 5 d for measurements and 2 d transition between periods). Goats were allocated to one of four treatments in a 2 × 2 factorial arrangement. Factors were no oil (CON) or 4% of soybean oil (SBO), and controlled thermal neutral (TN; 15 to 20 °C) or heat stress (HS; 12 h/d at 37 °C and 12 h/d at 30 °C) conditions. This resulted in four treatment combinations: TN-CON, TN-SBO, HS-CON, and HS-SBO. Compared to TN, HS goats experienced lower (p < 0.05) feed intake, body weight, N retention, milk yield, and milk protein and lactose contents. However, goats in HS conditions had greater (p < 0.05) digestibility coefficients (+5.1, +5.2, +4.6, +7.0, and +8.9 points for dry matter, organic matter, crude protein, neutral detergent fiber, and acid detergent fiber, respectively) than TN goats. The response to SBO had the same magnitude in TN and HS conditions. Supplementation with SBO had no effects on feed intake, milk yield, or milk protein content. However, SBO supplementation increased (p < 0.05) blood non-esterified fatty acids by 50%, milk fat by 29%, and conjugated linoleic acid by 360%. In conclusion, feeding 4% SBO to dairy goats was a useful strategy to increase milk fat and conjugated linoleic acid without any negative effects on intake, milk yield, or milk protein content. These beneficial effects were obtained regardless goats were in TN or HS conditions.