We have a setup like below on each of our two back porches. Kitty Tube with a Rubbermaid tub on top. The platform has PVC legs and is clipped at 45° across the front to align with the tube opening. As we call it.... The platform is the "veranda" and the tub is the "cabana".
The Kitty Tube is insulated and ventilated. They're really nice but you're probably not going to like the price. Available from Kitty Tube or on Amazon. Free shipping though.
We did these shelters after we adopted 4 ferals (or, they adopted us) in 2012 and knew they were going to be keepers. We still have 2 of them. One had given birth to her second (that we know of) litter when we found her. Pretty amazing for ferals to make it to 15 years old now.
If you keep the cat, you should look into TNR (Trap, Neuter, Return) services near you. Likely much less expensive than a local vet unless they offer some type of deal. That's what we did with ours. Fresno appears to have 3-4 offerings.
Good luck!!
The Kitty Tube is the warmest fully insulated outdoor house for your outdoor cat!
www.thekittytube.com