WHAT THE EXPRETION "CORE-BORED" MEANS

HYUNDAI is driver on left side USA?
your are barking up the wrong tree, the heater core is at 180f+
so there is no reason at all to be in the engine bay period.
we can Cal also IR gun the 2 firewall tubes to core and see 180f
and both hot means the core is working 100%
one side hot told you the heater core if fully hot so believe it.
what fails is simple the dampers.
called blend damper doors and motors.and 3 causes
the service manuals shows the tests. easy if your read it.
1: damper shaft (hinge) turns fully and free is good.
2; then we test the damper motor, see if it swings fully or not.
if not it is bad, if dead, it is dead or controls are dead. to it
3: testing the controls is harder, lots more. but in the manual I refuse to reprint,
we must test all doors there dampers.
mode failing,
recircc/fresh air door
blind door
some cars have 2 blind doors, left and right. like jeep commanders do.
there are 4 damper here, top to bottom in SM
floor door
vent door
temp door
defrost door
there is 12 part I see there, a floor door leaver but AC cold works so not that.
I see no dual blend damper. on this car
is heat good to all other ports, even glass defrost up top.

now the strange stuff, in fact just happened to me, costy
the cores can clop up 2ways. both inside hot water and outside fins or both, in such a way as only one side makes heat,
I used a bore scope CA'M to find mine, and right side was packed on green rust on the heater core. to be honest , the distrubution boxes
here can be partitioned oddly, and cause what I had wrong above

on my car , the blend door hinge is split bug is ganged, and if the center hinge breaks I will loose all heat to right side.
a $2000 fix too. 10 hours labor.
so doing all tests is what matters, and guessing not.
my post shows all the ways i've seen,
in some case parts that need to be seen can not,
there are youtube posters showing drilling 8mm holes casings to view doors with Bore scopes. Camera.
for dead doors.(damper or 1/2 dead)

or this kids stuff wads of papers into vents?
if AC fails or is weak make sure the drain is not cogged up or evap core goes underwater and fullyfails or just half fails.. or floods the floors.

If it's in your car I can think of this your heater core is bad. Heater core is a small radiator inside your car for a/c heater system.
The other thing I can think of you might have rotten metal where oxidation got to it. Under the carpet would be the problem and it gets in when your wheels kick up moisture from the ground as you drive.

One side only or both? Do you have a sunroof? Clogged drain vent for sunroof, cowl, A/C, bad weatherstrip?

If you mean back floor it has a window seal leak or a bottom plug...Most vehicles have plugs under floor for draining purposes...The plug could be missing or needs to be sealed.....If it is the front floorboard it should be the heater core leaking or plug as well...But normally it is heater core

i believe that means you have a blow heater coil

You more than likely have a bad heater core. Assuming by water you mean engine coolant, if it is just water than your AC drain hose probably came unhooked, but im pretty sure if that was the case than the water would be on the passenger floor. If your radiator is also losing water its the haeter core.

CORE PLUGS HARD TO REACH THEY ARE ON SIDE OF CYLINDER BLOCK.ENGINE HAS TO BE REMOVED BEFORE YOU CAN REACH REPLACE CORE PLUG.TO CHANGE CORE PLUG YOU CAN USE A HAMMER AND A LARGE PUNCH.KNOCK CORE PLUG SIDEWAYS IN BORE.PULL CORE PLUG OUT WITH PLIERS.WHEN INSTALLING NEW CORE PLUG IN BORE.MAKE SURE INSIDE BORE CLEAN FREE FROM RUST.USE SCOTCH BRITE INSIDE BORE.ROTATE SCOTCH CLOCK WISE POSITION TO REMOVE RUST INSIDE BORE BE CAREFUL DONT DAMAGE SCRATCH INSIDE THE BORE.THEN CLEAN INSIDE BORE WITH ACETONE.REMOVE RUST AND GRIME.WHEN YOU SEE CLEAN DRY METAL SURFACE.COAT THE SEALING SURFACE OF CORE PLUG WITH A NON HARDENING SEALANT LIKE PERMATEX NUMBER 2 .DRIVE NEW CORE PLUG IN PLACE WITH A LARGE 1/2 INCH SOCKET AND 1/2 INCH EXTENSION IF YOU DONT HAVE A DRIVER SET.YOU ARE DONE.

Check heater core hoses thats where they are you just may need to tighten but check the pipe fittings to core and check if the inside floor wet middle passanger side that would mean the core is leaking

that means your heater core is bad. It is not hard to fix but it is time consuming. Heater core is located behind glove box