Thanks everyone for your answers!
So, looking at Shane’s response and relating it to basic affiliate links on your site, you advise to stick with 301 redirects. I suppose, when redirecting your visitors to a betting site, it’s permanent rather than a temporary redirection.
Well, in regards to my comment that “too many” 307s on a site may have a negative impact, I’m basing it on the advice some SEO agency gave me and also it is flagged as a “Warning” with tools such as SEOmoz.
Thanks again!