You're screwed. Tranny fluid is designed to be extremely viscous regardless of the temperature of the transmission. It's really 90w oil. Your dot 3 is 30 weight oil. Your brakes now don't work because the 90w oil won't lighten up when it warms up so you've filled your braking system with thick stuff. Think of it like putting maple syrup in the fridge. If your maple syrup flows nicely at room temp, then you put it in the fridge, that's like adding 90w. Doesn't flow so well now, which means the brake oil won't flow into the piston.
I'm suprised you haven't blown a brake line, frankly. I would flush and fill the system ASAP.How to fix brakes on an 81 ford sedan...?
OK, that was a dumb thing to do. Let's just get that out of the way. Never put anything into the brake system other than DOT approved brake fluid.
Yes, there is trans fluid still in the lines. You will need to flush the entire brake system, from the master cyl to each wheel. If you know how to bleed brakes, you can do this. Get a big bottle of DOT 3 (or better) brake fluid and flush everything. Hopefully the trans fluid has not damaged any braking components, otherwise you have just trashed your brake system.