In this fantasy novel I'm working on, the villain is from a very cold-climate planet and is planning an invasion of a much warmer planet. While most of his army is standard infantry and cavalry, he also depends on a number of war mammoths to break though enemy lines. The problem is, mammoths are extremely furry and filled with subcutaneous fat to keep them warm in freezing temperatures, and the planet they are invading is tropical in the north, desert and Mediterranean in the center, and temperate in the south. This would mean that most of his mammoths would die of heatstroke before they ever saw battle. How could he or anyone else prepare or adjust cold-climate war animals such as mammoths for the invasion of a warm area so this doesn't happen?
These mammoths are fully domesticated so they don't freak out in the middle of battle like real-life war elephants.
Space travel is done via magic rather than technology in this universe, but for complex reasons I have no time to explain, the magic system wouldn't be of any help here. The technology of both parties involved in this invasion is pretty much medieval.