A major obstacle for optical clocks is the frequency shift due to black body radiation. We discuss how one can tackle this problem in an optical lattice clock; in our case 87 Sr: firstly, by a measurement of the dc Stark shift of the clock transition and, secondly, by interrogating the atoms in a cryogenic environment. Both approaches rely on transporting ultracold atoms over several cm within a probe cycle. We evaluate this approach of mechanically moving the optical lattice and conclude that it is feasible to transport the atoms over 50 mm within 300 ms. With this transport a dc Stark shift measurement will allow to reduce the contribution of the blackbody radiation to the fractional uncertainty below 2 × 10 −17 at room temperature by improving the shift coefficient known only from atomic structure calculations up to now. We propose a cryogenic environment at 77 K that will reduce this contribution to few parts in 10 −18 .