Hey bro, I just got this case in the mail last night
Fanbiya Armor Case for ASUS ROG Phone 5 - TPU Case with Clear Back, Compatible with Aerocooler and Air Trigger, Rugged Protective Cover (Case with Clear Tempered Glass)
LOVE IT so far, seriously can't recommend it enough. That MME case looks like the same thing so you'd probably be happy with it too, but I can't speak directly to it as I don't own it
https://smile.amazon.com/gp/product/B093BYQ3MX/ref=ppx_yo_dt_b_asin_title_o06_s00?ie=UTF8&th=1
I bought this. Took about 2 weeks to arrive from china. I don't have a cooler but even if I do, it won't cool it efficiently since the phone is behind a plastic.
This is the one I'm currently using:
https://www.amazon.com/gp/product/B093BYQ3MX/ref=ppx_yo_dt_b_asin_title_o06_s00?ie=UTF8&psc=1
It's excellent and feels like a cheaper otterbox, but I also wanted something stronger so I went and ordered this one: https://www.amazon.com/gp/product/B09DYJS2MH/ref=ppx_yo_dt_b_asin_title_o02_s00?ie=UTF8&psc=1
I haven't received the second one but it reminds me of my old otterbox defender. I can update you when it gets delivered but the first link I posted is excellent as well. I work construction and haven't had any problems. I've only had it for a month but it's doing its job for now. There aren't many cases for this phone, as you can probably tell.