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The coolant valve to the heater sits above the heater matrix on the inlet pipes. It can be accessed from under the bonnet near the bulkhead below the windscreen.
The heater matrix can be accessed from the front passenger side. Remove the glove box and the flow end return pipes for the heater matrix can be seen. You will need a fairly long T20. Torx driver.
You would have a leak, from either the pipes to the heater matrix (radiator), or the matrix itself.
the heater matrix is blocked
No most certainly not. In most countries this is illegal and you will be prosecuted if found guilty. Always use metallic pipes for hot water, inlet or outlet.
Remove centre consul. Drain cooling system. Remove 2 heater pipes on bulk head under bonnet. Remove matrix cover in car under dash. Pull matrix out. This was on a 2002 model. As they say in the haynes manual..do in reverse to refit !
The heater matrix could be blocked. Best option is to disconnect the two pipes going to the matrix, first finding the flow pipe (put your hand on the pipes to find the hottest one.) Once disconnected, backflush with a garden hose by putting it on the return pipe (the cooler one), and turn on the hose, flushing the matrix. Reconnect the hoses refill system.
Check the heater matrix, and any other heater related pipes that may be leaking. Or it could just be a leaking door seal.
There is two pipes on the right side of the engine bay that connect to the heater matrix itself inside the car, disconnect the two pipes. go inside the car and into the passenger side foot well, unscrew two Philips screws on the heater matrix housing directly behind the centre console once the cover is removed you should be able to have a little play to move the heater matrix in and out, two bolts either side of the gearstick housing should give the housing more room for play and removal is complete.
Acabin air filter (if fitted) could be blocked. The heater matrix or pipes to it could be furred up. A cooling system flushing treatment might do the trick. Failing that a strip out and cleaning the crud from between the matrix fins might be the answer. If all else fails a new matrix might be required.
The dealer.
it is located behind the dash in the middle. you can get a better idea of its location by finding the core's inlet/outlet pipes in the MR2's front trunk.