An isolation assembly for downhole injection use is described that features at least one isolation device mounted on a tubular so that when injection fluid changes the tubular temperature which can cause a length change in the tubular, an anchor for the tubular is provided to resist such a dimension change. The result is that the isolation device such as a packer can be left undamaged and retaining its sealing integrity. The anchor can be an inflatable or telescoping pistons disposed to grab in open hole. When using telescoping pistons, their placement on the liner and their pattern can meet the desired locations where grip is enhanced. Use of cement inflatable anchors is contemplated as an alternative.