So this is possibly not going to be fun. I have the same issue on my '02 Montero Limited. The way the heater core is set up, the air passes through the evaporator core first then the heater core. The heater core is flat and rectangular sitting lengthwise left to right, and the left (driver's side) of the core feeds primarily the left vents and the right side of the core feeds the right vents, but there is no air divider above the core, it is just a fairly small space and the air flows toward the paths of least resistance. Both heater tubes enter and exit the core from the left side, so the right side is usually the culprit. This reportedly is the highest spot in the vehicle and most likely place to get an air pocket. It also is a likely spot to get a core blockage which requires replacement and the entire dash removal. The "cold" side of the heater core has air flowing through it into the passenger compartment without getting heated by the core.
Consider getting a radiator funnel and filling coolant level with heater(s) full on and steady rpms above 1,800 or so while watching for air bubbles in the radiator funnel. Keep this up with rest breaks of "engine off" intervals for a period of time until you are confident there are no more air bubbles coming out. If you are lucky, it will be an air pocket and you can clear it and get the heat flowing to the right side again. If not, then hang on to your hat and schedule some major down time for a heater core swap, with complete dash removal. It is not for the faint of heart. I will likely just bundle up until Spring when I feel froggy enough to pull the dash on mine. Good Luck.
Resource:
Montero Heater Core JustAnswer Dougc