Nick...there are some good suggestions that have been made...I will offer another one if you are mechanically inclined...this may be a long post since I am known to ramble a bit...
from looking at your picture, I would guess the area you are working with is ~8' long and 22" or so wide...it would be so easy to go to home depot, buy some light plywood like 1/4" thick and enclose your grow area completely...make a frame out of 2" X 2"s and use 1/2-5/8" deck screws (or something like them) to secure the plywood to the 2" X 2"s....then all you have to do is make your access...very easy...figure where you want your access to be...then cut out the "doors"...if you like plexiglass, you could get a couple of pieces and make your doors out of them using the pieces you cut out as "templates"..then drill holes in the plexiglass for your hinge "hardware"...I know the light may be an issue, but I don't see it that way...if you make the "box" out wood, you could mount ceramic light fixtures and screw them into the wood...wiring will be another thing...easy but I won't explain here...then get some 42 watt CFLs (2700K bulbs are cheap)...this allows you to have as many lumens/ft[sub]2[/sub] as you desire...IMO you don't need more than 1000-1200 lumens/ft[sup]2[/sup] for good early growth seedlings...
if you decide to do this, just watch what you are doing with the wiring, the ceramic fixtures won't get too hot for the wood, so fire shouldn't be a problem unless you overload the light fixtures or wiring...(read: use a huge wattage light bulb as in over 150W or so)
I don't know why bu t building something that is easy, functional, and most of the time cheap sure does make me smile....
there are many ways to go if you want to control the temperature in a "contained" area...I have seen good looking setups that are made out of PVC pipe, and that is easier than plywood and 2 X 2s...people have taken commercial shelving and closed that in with visquene (6 mil plastic) with a 4' shoplight on each shelf...
I don't know how long you are going to grow inside, but, to me I will tell you it is a pain in the ass...lot's of work....if you are going to grow inside to maturity, that is a whole other can of worms...and the biggest is your electric bill...during January to March, I run nearly 3.5K watts 24/7 and that eats me up...of course, that is for about 1500 plants in all stages of growth...if you ARE going to grow inside, I really recommend building an area that you can germinate seeds, grow seedlings fast, then a "slow grow" area....
it has taken me several years to get my grow set up like I want it...I have a germination chamber 2' X 2' X 4' (holds 8 72 cell trays), a fast grow area that will also hold 8 72 cell trays (3K lumens/ft[sup]2[/sup]) and a slow grow area that is 3 20" x 8' shelves and where I keep the plants until they reach about 12" tall if needed..this area will hold 24 trays, they will be in 3" square containers when they hit this area and if they get too big for the slow grow area, it is almost time for plantout...
timing of starting the seeds is of utmost importance...you have to look at when your last frost is and back up 8-12 weeks before...shorter period for annumms and longer period for chinense...
just remember to have fun with your hobby...I forgot that and what I was doing became work...hell, I am retired and I just want to enjoy my life...
you know, I just read what I posted and boy, was I off...but I am not going to delete it...
temperature control is the most important thing for seed germination...I use thermostats and light bulbs...the CFLS put off enough heat to warm the area if it is enclosed...