The constraint satisfaction problem (CSP) of a first-order theory T is the computational problem of deciding whether a given conjunction of atomic formulas is satisfiable in some model of T . We study the computational complexity of CSP(T ₁ ∪ T ₂) where T ₁ and T ₂ are theories with disjoint finite relational signatures. We prove that if T ₁ and T ₂ are the theories of temporal structures, i.e., structures where all relations have a first-order definition in (Q; <), then CSP(T ₁ ∪ T ₂) is in P or NP-complete. To this end we prove a purely algebraic statement about the structure of the lattice of locally closed clones over the domain Q that contain Aut(Q; <).