Low-temperature specific heat of Heisenberg-Ising ring at | Δ| ≪ 1 is calculated by the method of non-linear integral equations. Specific heat in constant magnetic field (CH) is proportional to temperature (T) at |2µ0H| ≪ (1+Δ)J. In particular lim H →0 lim T →0CH/T is 2θ/(3Jsin θ) where θ= cos -1Δ, ≤θ≪ π. It is conjectured that lim T→0 lim H→0CH/T = lim H→0 lim T→0CH/T from the result of numerical calculation. Low-temperature specific heat of the one-dimensional X-Y-Z model is proportional to T-3/2 exp (-α/T) in the case of Jz > Jy > 0, Jy ≧Jx > -Jy.