  Generation of random thermal particle momenta is a basic task in many
problems, such as microscopic studies of equilibrium and transport properties
of systems, or the conversion of a fluid to particles. In heavy-ion physics,
the (in)efficiency of the algorithm matters particularly in hybrid
hydrodynamics + hadronic transport calculations. With popular software
packages, such as UrQMD 3.3p1 or THERMINATOR, it can still take ten hours to
generate particles for a single Pb+Pb "event" at the LHC from fluid dynamics
output. Below I describe reasonably efficient simple algorithms using the MPC
package, which should help speed momentum generation up by at least one order
of magnitude.
  It is likely that this wheel has been reinvented many times instead of reuse,
so there may very well exist older and/or better algorithms that I am not aware
of (MPC has been around only since 2000). The main goal here is to encourage
practitioners to use available efficient routines, and offer a few practical
solutions.
