What legal recourse do I have if repairs promised by the home seller were never made?
A contract for the purchase of a home is just that - a contract. It is legally binding on the home sellers who agreed to make the repair. As such, you may have a few different options.
Options for a Home Seller's Breach of Contract
The first and easiest option is to contact your real estate agent and/or the real estate agent who represented the sellers. There may have been money placed into an escrow account for the repair that can be paid out to you. This would allow you to get the problem resolved quickly.
If there was no money in the escrow account, or no escrow account, then your only other recourse is to file a court action against the sellers. You could potentially file such an action for "specific performance" to compel them to fix the furnace, however this is probably not the best way to go because then you'll be stuck with a house that has a broken furnace for the duration of the court case.
If you can't wait around for the case to play out while you have no furnace, you'll have to bite the bullet and fix it yourself. If you decide on this option, then you'll file a civil suit to get back the money you paid out to fix the furnace. This money that you spend is considered to be "damages" for the seller's breach of contract and as long as you keep careful records of the money paid out, you keep the costs reasonable, and you really did have a legally valid contract, then you have a good chance of winning your case and having the sellers pay out.
Getting Help When a Home Seller Breaches the Contract
If you do intend to pursue a breach of contract case, it is in your best interests to consult with an attorney for guidance and advice.