I could not agree more. Every where I've lived a cracked heat exchanger = condemned furnace, period. Get a legit HVAC tech over there ASAP to condemn the unit. Notify the "home warranty" company they have 24 hours to change out the furnace under warranty or there will be legal consequences. When they fail to do so have it changed out. If necessary finance it through the HVAC company or the gas company which ever is best for you. Document everything especially the notice to the HW outfit. E-mail them and/or send the notice via registered mail, or both.
Then prepare for a civil suit, no I'm not kidding. See if it could be heard in small claims court. The size of the suit all depends on the state you live in. If you have to go to civil court get an attorney and make sure the settlement includes all court costs & attorney fees.
There will be those who insist its not worth the suit, but think about all the other people who will get screwed over if they are not held to the contract. When I had a car wreck about 3 yrs ago the only way I could get the SOB's at the offending driver's insurance company off dead center was by hiring an attorney.
I too had a home warranty purchased by the previous owners. Not worth the trouble. When I had some plumbing issues they would not even send someone to look. I made the repairs myself and told them to F off when they tried to sell me additional coverage.