  We investigate the thermodynamics of Gauss-Bonnet black holes in
asymptotically de Sitter spacetimes embedded in an isothermal cavity, via a
Euclidean action approach. We consider both charged and uncharged black holes,
working in the extended phase space where the cosmological constant is treated
as a thermodynamic pressure. We examine the phase structure of these black
holes through their free energy. In the uncharged case, we find both
Hawking-Page and small-to-large black hole phase transitions, whose character
depends on the sign of the Gauss-Bonnet coupling. In the charged case, we
demonstrate the presence of a swallowtube, signaling a compact region in phase
space where a small-to-large black hole transition occurs.
