* Overheating Engine: If your engine is overheating, the increased demand placed on it during acceleration could cause the cabin heater to blow hot air. The engine's cooling system may be compromised (low coolant, faulty thermostat, clogged radiator, water pump failure). This is a serious problem and requires immediate attention.
* Blend Door Actuator: This small motor controls the flow of hot and cold air. If it's malfunctioning, it might be stuck in the hot air position, or its operation might be affected by the increased engine load during acceleration.
* HVAC System Issues: Problems within the HVAC (Heating, Ventilation, and Air Conditioning) system itself, such as a faulty temperature sensor or a malfunctioning blower motor resistor, could lead to inaccurate temperature control, especially under stress (acceleration).
* Coolant Leaks: A leak in the cooling system can cause the engine to overheat, leading to hot air blowing from the vents. The increased engine demand while accelerating exacerbates this problem.
* Transmission Issues (Less Likely): While less common, severe transmission problems causing overheating could indirectly affect the HVAC system by drawing extra power from the engine, leading to higher coolant temperatures.
In short, the hot air is a *symptom*, not the cause. The underlying cause is almost certainly an overheating engine or a fault in the HVAC system. You should not continue driving the vehicle with this problem. Overheating can cause serious engine damage. Have a qualified mechanic diagnose and repair the issue immediately.