Yeah the small talk part is key, but you can't let it drag on. Accept the drink but find a way to get back to the furnace pretty quick, that's how it pays off.
Totally agree, turning it down is just awkward for no reason. I had a mechanic offer me a soda once while he looked at my car, and we chatted about the game that was on his radio. Later he threw in a wiper blade for free, just because. That five minute chat made it feel like we were on the same team, not a transaction.
Honestly taking the drink is the smart move here. Turning it down just makes things awkward right from the start. That person is trying to be friendly and a little small talk over a coffee can make them more willing to do a solid for you later. You get better service from someone who feels like you're a normal person, not just a customer. It sets a cooperative tone that might save you money or get you a quicker fix.