Might be a bit cool for them in the 50s. If you can put some indirect heat in the coop (in case they need it), you might do so.
Chicks, in the absence of a mother hen to keep them warm, need an ambient of about 95 degrees their 1st week, 90 the 2nd week, 85 the 3rd week, and so on. At 4 weeks, they need about 80 degrees.
Like you, however, we've found those are pretty much just guidelines, and we've had chicks spend time in temperatures that were 20 degrees or more below their "guideline", but we monitored them closely in that time, taking them back to a heat source if they started showing signs of being cold (huddling together, shaking, etc).
In a coop overnight, that might be too long a period in cold weather without the heat source.
Word of caution: if putting a heat source in the coop, be very sure that you're not creating a fire hazard: no flames, no red-hot heating elements, heater fully secured to something (floor/wall) so it won't fall OR an emergency cutoff should it topple, etc. We use small, ceramic heaters for brooder heat and coop heat.
Let us know how the move goes
