What are some techniques I can use to reduce the dejection that comes from a "Thanks, but no thanks" e-mail from these positions?
For me the worst part of getting rejected for a job is feeling worthless, like I'm not good at anything. To fight that specifically, I recommend spending time with friends. If you feel comfortable directly telling them that you're having a shitty time and could use some encouragement, definitely do that.
If you can, do something nice for someone. Email a friend you haven't seen for a while and ask how they're doing, volunteer for something if you have the opportunity - this doesn't have to be in person, if there are any communities for newbies in your field, join them and answer questions, heck, just offer to help someone with their bags. The idea is to remind yourself that you have something to offer.
If you like doing anything creative, do that. If you can create something, whether that's a meal, a blog post, a set of shelves, a knitted scarf, a painting, that proves that you matter because now there's something where there used to be nothing.
Like other commentors have said, distraction is a good idea too. Take a break and do something fun. With friends if everyone's schedules allow, if not it's totally fine to spend an evening watching netflix, playing games, whatever works for you.
And you know, sometimes you just need to feel your feelings until you're done. Rejection sucks, it's okay to feel bad about it. Maybe you need an evening watching sad movies and eating icecream and just being sad until you get bored of it (being sad is actually really dull, it won't take as long as you think).
Don't forget that the people rejecting you for jobs have tons of applicants for every job and they're not judging you personally, they're judging your resume/cover letter by taking a quick glance at it. I help review resumes at my work and I'm sure I've rejected good people who just had bad resumes. Even if your resume is great, someone else's might be fantastic and just happen to be perfectly suited for that particular job. A huge part of job hunting is luck and numbers. Heck, maybe your resume is amazing but the hiring manager wants to hire a friend of theirs, or doesn't like the school you went to, or you just happened to use their least favourite buzzword.