Apple Coverage on Carrier Replaced iPhones

Here is Apple's iPhone warranty (in the U.S.):

http://www.apple.com/legal/warranty/products/ios-warranty-document-us.html

When Apple offers a replacement unit, that unit is warrantied for thirty days or until the original device's warranty expires, whichever is longer.

The above is true for replacement units provided by Apple or Authorized Apple Service Providers. If your carrier has replaced the iPhone, I recommend you see if they are an Authorized Apple Service Provider. And read the warranty carefully for yourself, as I am not an authority, I do not work for Apple, and I am not a lawyer. And, as I say, if you are not in the U.S., your country may have different provisions.

In you original post, you asked about carrier replacement.

Now you mention third party replacement. Which do you mean?

Again, if the carrier is authorized to do Apple service, you should be fine.

A third party (which I interpret as unauthorized) replacement will likely leave you out there on your own.

The only units that will be honored by Apple are ones they replace in or out of warranty, or that are replaced in or out of warranty by Carriers authorized by Apple to act as service providers.

If you had a phone replaced by a 3rd party insurance program through your carrier, no, that device will not be warrantied by Apple. Any further responsibility for that replacement device would fall on the insurer - see if they offer any guarantee with their replacement device(s). They may still provide for-fee out of warranty service on it though.