Roses can be transplanted any time of year as long as the soil can be
worked. I have moved roses in the middle of winter when the soil was not
frozen, in the summer heat etc.

As mentioned in previous responses, you must be able to water every day
after the move.

Keeping the root mass as intact as possible is probably the most important
detail. In the summer heat any plant is using a lot of water and the water
is taken up by the feeder roots. These are the fine, hair like structure
that are most easily damaged any time the rose is disturbed.

Removing a significant portion of the canes and foliage will help balance
the loss of the feeder roots. The more foliage on the rose, the more water
it demands, so balance the demand and the supply systems.

In the last month I moved a Sydonie and William Shakespere 2000 by carefully
digging and removing a great deal of foliage. They are both showing new
growth and appear to be healthy in their new home.

The move will 'set back' the size of the plant by 1-2 years as they recover
and produce a new root system. Using a root stimulator is advised as well
as feeding very sparingly. You don't feed a sick person steak, you give
them soup!

This isn't magic, just sensible and logical techniques.

Tim