Hyndai elantra heater blows cold and hot air.

This is the most likely reason

https://www.fixya.com/cars/r29872074-vehicle_cooling_system_no_heat

It could also be seized blend door actuators not directing the hot air. Or the switch unit.

https://www.google.com/search?q=2003+Hyundai+Elantra+heater+does+not+work

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check to make sure the blend door is changing from cold to hot. With the engine off and the key in the run position set the blower motor to the highest speed. Turn the temp dial to full cold and wait 30 seconds. Now turn the temp dial to full hot a listen carefully. You should hear a difference in sounds as the blend door sweeps through its full range.

If it is working and the engine is fully warmed up feel the heater hoses where the pass through the fire wall. One should be very hot and the other should be pretty warm. If one is hot and one is significantly cooler than either the heater core is plugged or there is air in the heater core causing a block in flow.

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

HEATER NOT BLOWING COLD,NO HOT AIR FROM HEATER,A/C BLOWS HOT AIR,A/C NOT BLOWING COLD, COLD AIR FROM HEATER,BLEND DOOR ACUTATOR CLOSED,HVAC UNIT NOT OPERATING,
http://alltypesofpartsreplacing.blogspot.com/2012/12/heater-not-blowing-coldno-hot-air-from.html

As per your problem mentioned.There are few solved help links to troubleshoot these problems.Go through the list and Click the link below:----
Air conditioner blows air but not cold air http://repairhelpcenter.blogspot.in/2012/07/air-conditioner-blows-air-but-not-cold.html

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Car overheats and Air blows hot at idle? http://howtobyme.blogspot.com/2011/11/car-overheats-and-air-blows-hot-at-idle.html

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Heater blows cold? http://schematicsdiagram.blogspot.in/2012/02/heater-blows-cold.html

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Heat blows cold on drivers side and hot on passenger side? http://schematicsdiagram.blogspot.com/2011/12/heat-blows-cold-on-drivers-side-and-hot.html---------- Hot air on the driver's side vents only? http://repairhelpcenter.blogspot.com/2012/01/hot-air-on-drivers-side-vents-only.html

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2005 Chrysler PT Cruiser: A/C Blows Warm? http://whoisbyme.blogspot.in/2012/06/2005-chrysler-pt-cruiser-ac-blows-warm.html

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1992 Toyota Camry: A/C Control light Flashing and A/C not Blowing Cold? http://technoanswers.blogspot.in/2012/04/1992-toyota-camry-ac-control-light.html

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No heat, blower blows only cold? http://technoanswers.blogspot.in/2012/02/no-heatblower-blows-only-cold.html

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These will help.
Thanks.

To troubleshoot this types of problem,click the link below :----http://howtobyme.blogspot.in/2012/02/heater-blows-only-from-defrost.html
--------Go through the procedure to confirm the issue.

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Engine Overheats and heater blowing cold?

http://howtobyme.blogspot.com/2011/11/engine-overheats-and-heater-blowing.html

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Heat blows cold on drivers side and hot on passenger side?

http://schematicsdiagram.blogspot.com/2011/12/heat-blows-cold-on-drivers-side-and-hot.html

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This will help.Thanks.

For this types of problem,i suggest you to check this help links:----Car heater blowing warm, but not hot air?http://schematicsdiagram.blogspot.com/2011/12/car-heater-blowing-warm-but-not-hot-air.html
---------A/C, heater, defroster fan, not working?http://technoanswers.blogspot.in/2012/02/ac-heater-defroster-fan-not-working.html
--------Heater problem?http://technoanswers.blogspot.in/2012/02/heater-problem-on-isuzu-trooper.html
---------Engine Overheats and heater blowing cold?http://howtobyme.blogspot.com/2011/11/engine-overheats-and-heater-blowing.html
-----------Heat blows cold on drivers side and hot on passenger side?http://schematicsdiagram.blogspot.com/2011/12/heat-blows-cold-on-drivers-side-and-hot.html----------------This will help.Thanks.

check water level in the radiator (when cool or cold) if there is not antifreeze in the overflow then your running low fluid in the system

If the car is hot and the heater blows cold air your thermostat is stuck shut or your radiator is really low on water/antifreeze check when engine is cold hasn't been ran like overnight take off the radiator cap and if it is low add so antifreeze/water if heater still blows cold air or water level is ok your thermostat is stuck shut and needs to be replaced.

start with a thermostat...

sounds like the heat blend cable is either dislodged or frozen, the cable runs from the control head to the blend door located on the drivers side just above the gas pedal ,it is not an easy job to replace, i sugest to take it to your local dealer, its not that costly and they will know exactly what to fix.