You don't typically get specific performance in most cases of breach of contract involving goods that are not unique. If money damages are an adequate remedy for the breach then generally specific performance will not be available. Thus, in most cases specific performance is not an available remedy for a breach of a product service warranty. In general, the damages you have for failure to honor a product service warranty are the cost of repairs or the cost to replace the unit, whichever is lower. Others have already addressed the issues relating to suing for reimbursement of the warranty cost.
Allow me to play Devil's advocate.
Lets say a dishonest individual starts a 3rd party warranty company and sells tons of warranties for everything.
Cars, refrigerators, electronics, etc... You name it.
However they refuse to honor any warranty.
Lawsuits cost so much money in legal fees, it may not be practical for anyone to really sue and the few that do, you only have to pay out what you were obligated what you were suppose to originally.
My family has received some aggressive phone calls for some auto warranty people and I wonder if there are doing this very thing.
Maybe these aftermarket warranty are a fool's bet if the company is not required to honor them unless compelled in an expensive lawsuit.