  In the strong coupling limit, $n$-point functions in lattice QCD with
staggered fermions can be rewritten exactly as sums over constrained
configurations of monomers, dimers, and baryon loops covering the spacetime
lattice. Worm algorithms provide efficient global sampling methods over such
ensembles, and are particularly efficient in the chiral limit. We study the
thermodynamics of strongly-coupled U(3) and SU(3) lattice QCD with one massless
staggered fermion using such methods, and compare the results with the
relativistic pion gas down to low temperatures O(15 MeV).
