Attenuation and quick ferment - first time all grain

Ok, so this is my first brew and my first post here, so if I miss something obvious, please give me some slack and constructive feedback. Thanks.

I'm interested in homebrewing because I want to save money and because I get a thrill out of doing things from scratch, so I went straight to all-grain brewing. I also kinda made my own recipe, which is almost a Dunkelweizen (I think.) My first batch is in the primary fermenter now. It only bubbled for 24 hours and now it seems to be done already. I carefully swirled up some yeast but did not notice any more activity after another 24 hours. It is under-attenuated, but only by about 3%, so I'm wondering if I should pitch more yeast or just leave it as is. Also, I made a silly mistake of not leaving any trub in the pot. I just swirled it all up and put it in the fermenter before I realized that I wasn't supposed to do that. I am using the brew in a bag method so it isn't as bad as it could be. I'm guessing that I can fix some of the damage by transferring to a secondary fermenter. Would that help with the sludge issue? If so, when should I transfer.

Nitty-gritty recipe and info is below.

Recipe for 3 gallon batch:
50 cups tap water
25 cups RO water
3.5 grams calcium chloride
4 lbs malted wheat
2 lbs pilsner
0.7 lbs Caramunich
0.15 lbs Cara malt special

I ground all the grain fresh at home with a Family living grain mill set on 4.2

strike temp 160 F
brew in a bag mash @154 for 60 minutes
iodine test passed

boiled for hot break and then added 0.5oz of 2.8% hops for 60 mins in hops bag.

OG was 1.059 (it was supposed to be 1.056)
Current FG is 1.018 (it is supposed to be 1.014)
-yep those numbers are already corrected for temp.

I cooled in a water bath and pitched a 1.5L (mostly drained) starter of WPL 550 belgian at 79 F (room temp). I was told by the guys at the store this strain would be ok at my room temp (I'm in Las Vegas and additional AC is hella expensive). I did put a wet towel around the sealed bucket to help with a little evaporative cooling for the first 48 hours.

So everything seems to be going great, except for the fact that I'm a bit confused by the quick and sudden fermentation. 24 hours after pitching it was done. I'm probably quibbling over minutia (a background in science will do that to you.) But, where is the line where you try to get fermentation going some more and when do you just leave it be? Should I be xfering to another container early considering the quick fermentation and the extra sludge in the fermenter?

Thanks for any help you can give a complete noob. It is greatly appreciated.

The WhiteLabs site says 68-78 degrees F for the optimum temperature, so you were a bit high at the start and most-likely went much higher. Active fermentation temperatures can go 5+ degrees higher than ambient, so although you used a towel I'd imagine you hit mid to low 80s (at least) for your temp. That would explain the rapid fermentation.

Temp control is one of the most important things you can do, so I would recommend looking into that before starting your next brew. A water bath is a cheap, easy, and effective solution.

How long has it been fermenting? I typically do not secondary anything. They will clear fine with time and all the trub just settles out and compacts at the bottom. Just don't stick your auto-siphon into the trub when you move to the bottling bucket. I just dump the whole kettle into the bucket and don't leave any trub behind so I think you are ok there. I would personally let it sit for a minimum of 2-3 weeks once at stable FG then go straight to bottle. If you can cold crash in a fridge for 24-48 hours prior to bottling then it will compact the trub even more and make for a clearer beer and easier transfer.

Just because you aren't getting any bubbling from the airlock doesn't mean the yeast aren't doing anything. It isn't uncommon for the ale yeast to go crazy with the easy sugars in wort but they make a lot of intermediate products then too which take them more time to break down and this break down process does not produce CO2. Give the yeast plenty of time for this step, another 2 weeks at least. That will also let them break down or absorb some of the off flavor compounds they produced too.

You didn't make a mistake by pouring all the wort into the fermenter. The hops and break material will settle first when the ferment slows down and then the dormant yeast will cover them. You don't need to go to secondary to clear the beer out, time in the primary will work just as well and that big amount of yeast that seems to be dormant at the bottom of the fermenter is still doing something good for you. Just being a little bit careful siphoning to the bottling will leave the yeast and hop material behind so you get clear beer.

Thanks for the tips! I'm very excited, it tastes pretty good already although a little cidery. I'll take your advice and just keep it in the primary for two weeks and then bottle. No more poking at it or worrying about it. I'll setup a secondary for another brew, perhaps.

So, seeing as I can't keep my house any cooler than 78-79 degrees, what is the best way to keep my fermenting bucket cool? Rajun50 suggested a water bath. I can do that, but I thought that was just to even out temperature variations, like if you are keeping it in a garage. Does it really make a difference if the water is the same as the air temperature and the house is already temperature controlled (albeit at a high temperature)? Don't the insulative properties of the plastic bucket make it difficult to cool externally? Would adding a sanitized ice pack inside create too large a temperature gradient? What do you do during the summer? Our summer lasts about 7 months.