  We study the low-temperature thermal conductivity (\kappa) of Dy_2Ti_2O_7 and
Yb_2Ti_2O_7 single crystals in magnetic fields up to 14 T along the [111],
[100] and [110] directions. The main experimental findings for Dy_2Ti_2O_7 are:
(i) the low-T \kappa(H) isotherms exhibit not only the step-like decreases at
the low-field (< 2 T) magnetic transitions but also obvious field dependencies
in high fields (> 7 T); (ii) at T \le 0.5 K, the \kappa(H) curves show
anisotropic irreversibility in low fields, that is, the \kappa(H) hysteresis
locates at the first-order transition with H \parallel [100] and [110], while
it locates between two successive transitions with H \parallel [111]; (iii) the
\kappa in the hysteresis loops for H \parallel [100] and [110] show an
extremely slow relaxation with the time constant of \sim 1000 min. The main
experimental findings for Yb_2Ti_2O_7 are: (i) the zero-field \kappa(T) show a
kink-like decrease at the first-order transition (\sim 200 mK) with decreasing
temperature; (ii) the low-T \kappa(H) isotherms show a decrease in low field
and a large enhancement in high fields; (iii) the low-T \kappa(H) curves show a
sharp minimum at 0.5 T for H \parallel [110] and [111]. The roles of monopole
excitations, field-induced transitions, spin fluctuations and magnetoelastic
coupling are discussed.
