Breach Of Warranty : 5 year parts & labor written warranty for heater / A/C system installed.

We had a heater installed 4 years ago in our home. It came with a 5 year parts and labor warranty. An intermittent issue came up with the heater last winter. The original installers attempted to fix the problem several times by replacing various small parts. They were never able to repair the heater. They then ignored repeated requests for service. We filed a complaint with the BBB. The company responded that there never was, nor is, a problem with the heater, and that they were basically done making service calls. We hired another heater company. They diagnosed and fixed the issue immediately. The heater manufacturer replaced the parts free of charge, but we had to pay this second company for the labor costs. The installing company, when shown the repair information, restated that they never witnessed a problem while on a service call, and that we are responsible for all costs associated with the repair. Can we recoup labor costs from the original installers?