Just make sure if you use a plate that you check what the temperature recommendations are for it (many recommend using in 50F and up only, so you still still need to heat the ambient air temperature around the plate in order to use it).
Don't tarp up too tightly so that there's no air, you want to buffer winds but there should still be ventilation available. As long as there's an part of the brooder large enough for the chicks to huddle that can maintain proper temperature (likely the section(s) away from the open sides) then...
What's the current high/lows of ambient temperature? What are the temperatures inside with the lamp on? The open part of the hutch, can the unit be reoriented or can the opening be buffered or partially blocked off to mitigate any draft?