I talked to my instructor today after reading this and becoming curious myself. We have not covered Aldols yet, but I'll share what she thought anyhow.
triethylamine acts as a base. With 2-phenyl-1-acetic acid (added numbers to make it clear), she proposed Step 1. (providing the acidic H+ is gone) triethylamine could remove 1 H+ from carbon #2. This intermediate could be stabalized by forming an alkene between C1 and C2 *C1 breaking a bond with the double bonded O) (though would need to revert back to undergo the next step). Step 2. Electron pair on Carbon #2 attack carbonyl carbon of thiophene-2-carbaldehyde (lets call this #3). Carbon #3 breaks one bond with it's oxygen, and the bond is formed. Step 3. The O on carbon #3 can by protonated (since there have been 2 hydrogens removed, maybe the environment is slightly acidic?). With heat, the OH on C3 and the remaining H on C2 could break off. OH takes its electrons, while H gives its electrons to form a double bond between C2 and C3, and the product has been formed.
My instructor was not sure how the acetic anhydride would come into play however. Yes, acetic anhydride is used in perkins reactions, and could react with the thiophene-2-carbaldehyde, but I do not know what good that would do. I dont know much about these, but I hope this would help, or at least put a person in the right direction.
If you guys figure out something more/something else, I'm interested now in knowing as well.