A320 Captain experienced both avionics fans (blower and extract) failure during climb. After ECAM actions and consultation with Maintenance flight continued to destination. Upon landing an avionics smoke ECAM is triggered and quick access to a gate was requested from the company and denied.

Narrative

Climbing through FL260 both vent and blower fan failed and respective ECAM appeared. Pilot not flying accomplished ECAM procedure; stopped climb at FL280; then; shortly [after]; FL290 for ATC. Contacted Dispatch and Maintenance Control; confirmed climb no problem FL370. I had avionics issue and pressurization issues on my mind; leveled FL330 final. Extract valve full open. Upon landing noticed ECAM avionics smoke. Informed ATC and requested emergency equipment in case. Requested gate to deplane passengers; refused by ramp. We parked and waited for complete inspection from Maintenance and firemen. ECAM completed by First Officer on ground. My personal conflict: no checklist on dual failure of fans; only individual which leads to possible avionics overheat should procedure fail to open extract valve. If one fan fails have backup-dual failure must be rare; couldn't find checklist-took extra time to make sure on my part. Avionics smoke ECAM on ground was real; not sensor issue; per mechanic; we went to internal cooling configuration after landing but no fans available! According to Maintenance 30 or more minutes and serious overheat would have begun. If in flight the valve didn't open it would have lead to issue. Problem 2--why were we prevented from getting to gate and exiting passengers? Had we smelled smoke we would have had to evacuate with slides. The terminal and jetway should not take priority over exiting passengers ASAP. We had 104 passengers and handicap passengers. I voiced my concern 3 times to ramp and was denied access to gate until trucks blocked us. Flight attendants were given information and performed professionally; passengers were warned on ground of possible evacuation. Fireman were great and overall procedures were accomplished smoothly Dispatch and Maintenance were clear and concise. I found checklist lacking info with no dual failure; which in my view should be analyzed. According to Maintenance a computer failure caused the fans to stop operating.