Will my wet carpets dry on their own if I put the heating on?
Quick answer: Usually no. Car carpets sit on thick foam underlay that can hold gallons of water, so cabin heat alone can take months or years to clear it. In the meantime mould, corrosion and electrical faults develop underneath. Small city cars with very thin carpets can sometimes air-dry over the summer, but you should still disinfect the cabin and check for damage.
People ask this because the top of the carpet feels dry after a day with the blowers on. The top isn't the problem. The foam underneath is.
Most drivers don't notice a leak until the car is already full of water, and there are often gallons of it sitting under the carpet. Cabin heating will eventually shift some of that, but "eventually" can mean years on a modern car, and by then the moisture has already caused water damage you can't see from the driver's seat -- rot in the floor pan, corrosion on connectors, and a musty smell that returns every time the weather warms up.
Why cabin heat alone doesn't dry the underlay
The carpet you see is a thin felt layer. Bonded to the underside of it, or laid loose on the floor pan, is a foam underlay several centimetres thick. That foam is designed for sound and thermal insulation, so it is deliberately open-celled and absorbent. Once it is saturated, it behaves like a sponge sitting on a metal tray.
Blown warm air from the heater only touches the top surface. For the foam to dry, the water has to migrate up through the carpet, evaporate into cabin air, and then leave the car through ventilation. On a car that is parked with the windows shut most of the time, that cycle barely happens. Lifting the carpet and drying the underlay directly is the only reliable way.
When air-drying can work
There are exceptions. On a small town car with very thin carpet and minimal underlay, a hot summer with the windows cracked open can sometimes get the cabin dry. Even then we would advise disinfecting the interior to keep mildew at bay and checking the floor pan and seat-belt anchor points for signs of corrosion.
The bigger issue is that air-drying only treats the symptom. If the water got in once, it will get in again the next time it rains hard. Finding and fixing the source matters more than drying the carpet.
If you also hear a sloshing or gurgling sound from inside the door when you corner after rain, that is a separate symptom -- blocked door drains rather than a carpet problem, though the drying process for both is the same. For the full detection process from first water test to dried car, see what does car water leak detection involve?