No. The eMachines e627 will only physically accept an S1 socket
processor. The Athlon X2 is an AM2 socket processor. You will need
to go with an AMD Turion X2. And even then some Turion X2
processors may not be supported by the BIOS. The AMD Turion X2
TL-50 should be supported and should be free of heat issues as the
dual core version of this laptop was shipped with this processor. I
have read of users successfully upgrading to the AMD Turion X2
TL-58 and TL-64 without issue. However, that is not first hand
knowledge on my part. I have the same laptop with the single core
TL-20 and am about to upgrade to the TL-64.