  We exhibit a theoretical calculation of the parameter \beta appearing in the
generalized uncertainty principle (GUP) with only a quadratic term in the
momentum. A specific numerical value is obtained by comparing the GUP-deformed
Unruh temperature with the one predicted within the framework of Caianiello's
theory of maximal acceleration. The physical meaning of this result is
discussed in connection with constraints on \beta previously fixed via both
theoretical and experimental approaches.
