The "Hot Stove League" is a baseball-related term, referring to the sport's off-season. The phrase does not denote an actual league, but instead calls up images of baseball fans, anxious for the start of the new season, gathering around a hot stove during the cold winter months discussing their favorite baseball teams. The term has also come to refer to the wave of off-season player transactions (trades, re-signings, free agency, etc.) that occur between seasons, especially during the winter meetings. Since most free agent signings and trades occur during the off-season, this time of significant player transactions (including rumors and speculation about possible trades), is often referred to as the "Hot Stove League" or sometimes more simply "Hot Stove". Essentially, teams continue competing, except it is the team owners and general managers who are doing the playing, with the score being in terms of human resource losses and gains.
The term is essentially an extension of the question, "What's cookin'?", since the off-season is the time-period when teams concoct their plans and rosters for the next season. The "Hot Stove" is where those plans are cooked up. Or, it could just refer to the sort of stove used to heat rooms, which is the sort of stove that people would gather around during winter months.