I think I may be getting the picture/message - this is an unmodified aircraft, that previously had no heating issues, that has recently started to exhibit overheating - correct?
Overheating, in Rotax 9's, is not usually associated with fuel (carburettors/ULP/AvGas) Unless you have somehow changed the carburettor settings to lean (reduced the fuel to air ratio) causing a hot burn. This would be reflected in high EGTs, probably hard starting, rough running near /at idle, light coloured plug electrode insulation and potential for knocking/preignition at shut down.
High oil temperatures, in a previously satisfactory cooling system, may be the result of reduced air flow over the cooler (contamination of cooling fins, deliberate or inadvertent partial/total blockage of air flow) reduced oil flow through the cooler (restriction/blockage due to air, collapsed pipe, internal build up of "sludge" )
High coolant temperatures - due to above problems and again due to external air flow/internal restrictions.
Correctly serviced Rotax 9 cooling systems should never need to be flushed. The same goes for oil systems (engine on ULP) BUT if abuse has occurred, or high percentage AvGas used, sludge in oil reticulation systems can occur & cause reduced oil flow.
Correct "purging" of both oil & cooling system must be done after every total drain/refill of liquids, to minimise the chance of an air lock in the system. Air lock will significantly reduce the ability of the coolant/oil cooling system to function correctly.
I am not sure what symptoms a partially blocked muffler might cause - speculation - hard starting, inability to idle at normal rpm, increased back pressure, poor combustion, low power and possibly heat due to combustion gases being retained for longer than normal.
