Yes. I would replace the thermostat first.
Judging engine flow is hard. Most of the tricks I know depend on experience for their use. One is to gently squeeze the top hose while reving to motor. If you feel the hose swell then the likelihood is that the radiator is restricted.
The fan clutch should be relatively firm when hot much more so than below its thermostatic temp. If you hold the engine at 2000rpm as the fan t-stat closes the noise the fan makes will get distintly louder as it speeds up.
Does your car have factory air? I have seen a number of non-US models with extremely small radiators not suitable for hot climates OR airconditioning.
Radiator flow/heat transfer problems are also hard to diagnose as it is a qualitative problem and judgement. I have seen many aluminum core radiators that must form enough of an insulative inner coating to not cool the motor but still flow good. Tough call, hopefully the thermstat fixes your problem.
Owner 24 bay BSC
Bosch Master, ASE master L1
26 years MB technician