Chrysler Repair: overheating Chrysler 300m, radiator core, radiator fans

Question
QUESTION: I have a Chrysler 300m and just replaced the engine 3.5L v6 .due to overheating the block was cracked .when I picked up the car with new engine the car started to overheat and a/c stopped working .I just refilled a/c too.so in the morning as I get up to go to work I warmed the car up and took off well about 1 mile away the car starts steaming and its coming from reservoir tank I  just changed thermal stat sensor there are no leaks what could the problem be

ANSWER: Hi Frank,
You didn't mention the year model so do let me know that in a follow-up question.
I would assume that engine replacement involved a new water pump also so presuming that the engine, waterpump and thermostat are not the issue then the main suspect would be the radiator core which if that was not checked and was partially or fully blocked then that heat removal device would not be functioning to cool down the engine coolant. Did you notice whether the temperature of the two sides of the radiator where similarly hot or was one side very hot and the other side cold? You may need a new radiator. Also, did you notice whether the radiator fans were running when the engine first overheated?
Please let me know the year model and any other information about the vehicle's history?
Please read the PS below.
Thanks,
Roland

---------- FOLLOW-UP ----------

QUESTION: 99 Chrysler 300M I replaced the fans after it overheated the first time but then it overheated again with the fanz working so I bought another engine cause it cracked the block and there was low compression. since then the fans and  thermal stat were changed I haven't noticed any leaks I didn't change water pump or radiator could that be a problem why it overheats also the timing belt was a little loose on the tensioner wasn't my mechanic suppose to check if water pump was still good and flush radiator

Answer
Hi Frank,
I am not clear as to what you meant by 'replace the engine, so it would be good to verify what its history is, and what parts were or were not replaced. But if the radiator was not at least checked to see that it had free flow of water through then that would be the first thing to check. Overheating so fast as you described raises that radiator question immediately. Again, what is the year of the car? And what is the history of the replacement engine as far as you can find out from the mechanic. The mechanic has not completed the job until he solves the overheating problem. So give it back to him now to work on.
Please rate my answer and consider giving a "yes" where you see the question about a nomination of me for 'volunteer of the month'.
Thanks,
Roland