Bleeding the system would include having it on a run with temp set at max so that the valves that control the flow to the heater matrix open fully and flush through air in the system.
On that line, not sure abut the mini but bmw setups have a electronic valve that controls how much coolant gets sent to the heater matrix. Is normally located on the inner owing. It’s possible for the wires and connection block to dry up a bit and loose the electrical join due to the proximity to the hot engine. A good waggle of the wires and connector can ensure a good voltage gets thro and helps the valve open.
Also internal temp sensor normally is a fan that draws air over the sensor in behind the control panel. The inlet vent can block up with dust and fluff. A good Hoover of the dash can suck that fluff out.