Enermax Staray (no internal or external fans)
Not a good idea to have no case fans with any build, there's many quality cases on Newegg, eBay & Amazon for around $50-60 (some less on promo) that includes at least one intake (most of mine two) & one exhaust, all 120mm fans. For any PC to remain cool, there must be a minimum of one exhaust & intake fan, if by chance a new case isn't in the budget, maybe a case mod can achieve the same result. Many has done this successfully, I forget where seen, there was once a site I visited that had blueprints for different sized fans. Even two 92mm fans are better than none, that's what's in my XPS 8700. Oddly, even though there's a place for the intake fan, one wasn't installed, so reused a 92mm CPU fan that was loud, using silicone washers to prevent vibration, installed & now can't hear, unless demand requires higher RPM. I use SpeedFan with this PC to control all fans, as Dell had it capped at just over 800 rpm. Had to use a PWM splitter leftover from one of my Noctua fans to install it, the only brand that I purchase.
My least expensive case at $49.99 shipped, a Rosewill Stryker M, has two 120mm intakes with blue neon lights, one exhaust, plus extra passive cooling with a screened top. looks fantastic in a darkened room & includes a plexiglass window to see the interior, although I turned the lighting effects off on the installed ASUS 970 Gaming/AURA MB. Also has a full modular EVGA G2 650W (Gold rated) PSU, was on promo on the Newegg site along with a $20 rebate, knocking the final price down to $69.99 shipped. The installed CPU is a AMD Phenom x4 965 (originally a FX-8350), moved the warmer running CPU to this MB because can handle the heat better than a mATX ASRock 970M Pro3 that the FX-8350 is running great on, inside of a slightly modded Dell Dimension 2400 case (can't see from the exterior), adding a 80mm Noctua PWM intake & 92mm exhaust fan from the stock FX-8350 CPU. The exhaust is connected via a PWM adapter to the CPU header.
Many who has seen what was once a stock Dimension 2400 stated it's by far the fastest they've ever laid eyes on & was once running W10 until the Fall Creator's update which messed up the Start Menu (odd because I had ran all of the Previews successfully. I just say that I know how to tune a PC to milk every last drop of performance out of one.
As others has mentioned, a quality PSU is a must have, it's the most important component of any build, inferior or older units can take out the entire system when these blows, so the cost can easily be much less than what you may think. If possible, try saving $10-15/month, in a few months, will have plenty for a much better model, preferably Gold rated & Fully modular to help with cable management. Many PSU's that says 'modular' still has the main cable to the MB built in, I prefer those w/out any installed, much easier to work with. Plan the install, being sure to connect the cables in the back first, working your way to the front, and tuck any extra length out of the way as you go. You'll love the end result.
If by chance you can't afford a new case, be looking on recycle days for those sitting on the curb, I've picked up a few this way & reused, still have one of the PC's to this day, although with a different MB, CPU & PSU. I reused the RAM, GPU & HDD's that were in the PC, removed one & now is another backup drive. Also, there's thrift stores that has computer cases at low prices, sometimes with fans & wiring harness already installed. You may be able to talk the asking price down some, especially at Goodwill & Hospice stores.