Either the a/c system is freezing up or you have a leaking heater core.............
If that smoke is more like steam, you have a leaky heater core.
Means that your heater core is leaking coolant. Has to be replaced.
The heater core has failed.
The blower resister is not supposed to be grounded. The smoke may be steam from a leaky heater core.
White smoke coming out of the heater vents in a 2003 Honda Accord could indicate a coolant leak, possibly due to a blown head gasket or a cracked engine block. When coolant enters the combustion chamber or the heating system, it vaporizes and produces white smoke. Another potential cause could be condensation build-up, especially in cold weather, but persistent white smoke usually suggests a more serious issue requiring immediate attention. It's advisable to have the vehicle inspected by a mechanic to diagnose and address the problem.
The smoke you see may be moisture/steam. The heater core is probably leaking engine coolant. If the "smoke" has a sweet smell to it, it's engine coolant. More info about the vehicle such as model and year would help.
Probably not smoke. Your heater core may have a small leak and the "smoke you see is actually steam.Had a similar problem with an F-250 P/U. Cost about $100.00 parts and labor. But that was back in the day...
could be a leaking heater core ( Steam ) . Depends on WHAT KIND OF SMOKE. Is it steam or smoke. Smoke like something burning could be oil. electrical, etc
heater fan broken.
Is it smoke or is it atomized freon leaking from the AC system? If it fogs the windshield and smells funny, you may have a leak in the AC/Heater system.
SOUNDS LIKE THE INTAKE GASKET BLEW, OR THE HEATER CORE FAILED.. EITHER WAY, THIS IS A COSTLY REPAIR.