Help! A3 '98 heating + AC failing

[Flyinge]

😊My mother in law has an older A3 (registration 1998). The heating and AC have both packed in. The quote to fix it is some €700. I don't know what this covers unfortunately, but it is barely worth it given the resale price of the car. Can anyone help me diagnose the issue (I'm adept at googling but know little about cars)?

• Problem with both AC and heating appears to have arisen at same time (we think)
• Fans appear to be blowing at normal power and fan power setting responds to changes
• When AC is on the air cools slightly, but not much
• When heating is on the air heats slightly, but not much
• The electronic display works and shows the target temperature

Given this, any ideas on the most likely issue? Could it be the thermostat? Or maybe the heater core (does this affect both AC and heating?)

Any ideas (and pointers to solutions) much appreciated...