The ram requires removal of the dash to replace the heater core. If it is not leaking I would try to flush it. My son just bought an Audi a4 and these are known to have issues with blocked heater cores. The solution that I found on the Audi forums is to back flush the core and use CLR Calcium, Lime Rust remover from Home Depot or Lowes. I have used Prestone radiator flush as well to clear out a severely plugged GM radiator after someone mixed green and red antifreeze but that is another topic altogether. CAUTION if you read the fine print on the CLR bottle it says not to use on aluminum or brass. I believe that this is because it will discolor the metal. I went ahead because there were so many good results posted and I was only going to leave it in for a limited period of time. I picked up some heater hose and used a garden hose repair kit to attach a female garden hose end to one side and connected the other side to the outlet of the heater core. Another length of hose from the inlet to the heater core to a bucket. Ran the hose and filled and emptied the bucket a few times and good amount of sediment came out. Next i lowered my compressor output to no more than 20 lbs. Remember the system is designed for 16 lbs and used an air nozzle to blow out the remaining water. Using a small funnel I poured the CLR unto the heater core until it came out the other hose. The directions called for a 50/50 CLR water mix but I figured any water left in the core would dilute it enough. I let it stand for about an hour and started flushing again. I alternated between water and low pressure air until the sediment stopped coming out. (AGAIN I caution about using air pressure, if the core is on its way out you will have a leaking core when you are done, this happened on a Firebird that I was trying to de-sludge but at that time I did not think to reduce the pressure and was forcing water through at 90 lbs of pressure)
From there top off the heater core with antifreeze, reconnect the heater hoses, check coolant level and hopefully you will have heat.
Scott