Used car purchase, engine condition – what now?

Hello the municipality, – with me there is a change of driving, in question 1-3 years old with max. 60tkm A4 with 2.8L, MB C220 or E220, everything wg. KOMBI and AHK, the 2 liter engines from VW or AUDI seem to me to be a little too weak for the performance > 170 hp. There are of private, leasing resetters, rent-returners, factory members, etc. All well so far. However, I am not quite sure that with friendly offers cars also motor- (among other things -) are technically checked so that one can If jd can give me a Paas tip here, it would be important for me: how do I recognize whether the engine is “heated”, i.e. usually driven with lead foot in cold engine before or vice versa, turbochargers were not cooled enough. At up to 60tkm it would be difficult for me to recognize. On the tyre profiles/optics of the tires would not be a VErlasse, which can also be replaced by any dealer, is also often done. I usually understand about the technology wa s, but here my possibility ends. Above all, it would be very unfavorable to drive 200 to 300 km to the next offer date and to have something checked there, respectively with DEKRA/expert. gruss and thank you for the contributions in advance