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you should clarify if you're telling people not to buy this card, or if you are asking for help on fixing it or if that generation video card suffers from problems, etc.
 
I bought a new graphic card witch is ATI Radeon HD 4870 1GB for mc pro 1st generation . I put it into PCIe slot but it's not run fine

when i started to working .. after several minutes my screen stopped and card overheat so much ???!!!
 
Probably a poorly seated heat sink or possibly some other defect. I would return it to the seller seeing that it has a 90 day warranty.

Also the card is not a genuine Mac edition of the 4870 but a general PC Card that has been flashed to work in Mac's. Seeing as it is a flashed card it may not be running the cooling fan at a high enough speed.
 
Did you actually pay $354 US dollars? It's only $349 from the Apple Store online, with free shipping. Although that card is the 512 version, it will work just fine.

Anyway, those cards do tend to run hot, but it sounds like the fan on your card isn't working right. Sounds like a problem with the firmware - may need to be reflashed to fix a fan problem.
 
I just checked today that the "fan" of my video card is not working !!
 
I just checked today that the "fan" of my video card is not working !!

Either the fan is outright broken, or the script used to flash your PC-version 4870 was bad and isn't controlling the fan properly. If you can return it, do so, but if not you might consider reflashing it yourself using the scripts posted here on MR for the 4870.
 
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