They wouldn't have replaced the processor, they would have replaced the whole LB. (The problem with iMacs was that the LB transistors couldn't take the ongoing current and eventually bulbed causing display anomalies and eventually failure.)
No need to worry about the paste, it will be a problem with the fans on the LB (as the LB would've been refurbed and potentially won't be an exact match to the original), or with an outdated OS, or a localised problem (environment, dust, etc).
They wouldn't have replaced the processor, they would have replaced the whole LB. (The problem with iMacs was that the LB transistors couldn't take the ongoing current and eventually bulbed causing display anomalies and eventually failure.)
No need to worry about the paste, it will be a problem with the fans on the LB (as the LB would've been refurbed and potentially won't be an exact match to the original), or with an outdated OS, or a localised problem (environment, dust, etc).