A MD80 flight crew received taxi routing clearance to their gate and crossed an intersecting runway without getting clearance as per the new procedure.

Narrative

Landed Runway 3 and cleared at Taxiway D. Tower cleared us to cross Runway 8/26 on Delta; left on Alpha and contact Ground. They did not tell us to hold short of Runway 17/35 and it was not in use for arrivals or departures. You know what's coming. Yes; I inferred from all of that that we were cleared to cross Runway 17/35. My First Officer and I proceeded to visually clear the runway in both directions and started to cross. By this time he had switched to Ground and before he could check in; Ground cleared us to cross Runway 17 and continue on Alpha to gate. I relied on our old verbiage; and the fact that these Controllers were not using Runway 17/35 that day. I should have held short and made sure we were cleared to cross. Also; because the airport diagram shows that Runway 17/35 comes up quickly once you make the left on Alpha; I should have appraised my First Officer to switch quickly to Ground once we cleared Runway 8/26. Stop short of all runways until you both hear; 'Cleared to cross Runway XX.'