Carriers add warmth on their own, since two bodies pressed together hold heat before the sun even gets involved. We dress our own kids in a single loose piece underneath: one of our double-layer muslin bodysuits or a short romper, nothing with a hood or a fleece lining. The open weave lets air move between fabric and skin, which matters more than how many layers you put on.
How that piece fits matters as much as the fabric itself. A romper that clings at the waist or ankles traps heat right where the carrier straps already press, so look for room to move rather than a snug fit; how muslin baby clothes should fit covers what that looks like in practice. Some parents skip clothing altogether under the wrap in favor of skin-to-skin, and how many layers a baby needs in hot weather walks through that trade-off, since a carrier changes the usual layering rules.
Babywearing usually means moving between outdoor heat and an air-conditioned shop or car, and that swing is where overheating and chilling both happen fast. Keep a light second piece nearby to add or remove rather than dressing for one extreme, and dressing a baby moving between air conditioning and outdoor heat covers how we handle that switch. Check the back of the neck and the skin under the carrier panel every so often: damp or flushed skin means it's time to loosen the wrap or find shade.