You know you can't 'melt' just a localized bit of ice. You have to tackle the entire problem holistically. Everything is connected to everything else, which means the only solution is planetary scale atmospheric geoengineering. Luckily planetary scale atmospheric geoengineering is a well understood and totally safe craft, so it's neither dangerous nor complicated for you to skew the entire world's climate for the sake of melting this one, admittedly quite large ice cube. You quickly cut up a few quadrillion tiny metal rods the exact length to scatter thermal energy (about a sixth of the width of a human hair) and scatter them around the atmosphere. Soon the temperatures rise enough to release the nice camp people. They all thank you and invite you over to have a hang with them, and while you don't have a plan just yet for removing these quadrillions of heating rods, you do feel satisfied you solved their problem, hopefully without causing any irreversible side-effects like a runaway atmospheric heating scenario.