The Miami Herald (Patrick Danner) reports:  The Miami Heat is putting a full-court press on premium-seat holders and sponsors it claims haven’t paid up. The Heat or affiliate Basketball Properties, which operates the AmericanAirlines Arena, have filed 16 lawsuits in the past year against companies and people they claim owe about $1.6 million — if not more. At least a few of the cases have been resolved. The Heat has taken the most litigious approach among South Florida sports franchises to force customers and clients to honor agreements. By comparison, the Florida Panthers and affiliate Arena Operating Co., which operates Sunrise’s BankAtlantic Center, filed three suits in 2008 to collect about $100,000.