My take on permanent versus temporary HTTP redirects in general
When I started digging into the HTTP world (which was around the time I started writing DWiki), the major practical difference between permanent and temporary HTTP redirects was that browsers aggressively cached permanent redirects. This meant that permanent redirects were somewhat of a footgun; if you got something wrong about the redirect or changed your mind later, you had a problem (and other people could create problems for you). While there are ways to clear permanent redirects in browsers, they're generally so intricate that you can't count on visitors to do them (here's one way to do it in Firefox).
(Since permanent redirects fix both that the source URL is being redirected and what the target URL is, they provide not one but two ways for what you thought was permanent and fixed to need to change. In a world where cool URLs change, permanence is a dangerous assumption.)
Also, back then in theory syndication feed readers, web search engines, and other things that care about the canonical URLs of things would use a permanent redirect as a sign to update what that was. This worked some of the time in some syndication feed readers for updating feed URLs, but definitely not always; software authors had to go out of their way to do this, and there were things that could go wrong (cf). Even back in the days I don't know if web search engines paid much attention to it as a signal.
All of this got me to use temporary redirections almost all of the time, even in situations where I thought that the redirection was probably permanent. That Apache and other things made temporary redirections the default also meant that it was somewhat easier to set up my redirects as temporary instead of permanent. Using temporary redirects potentially meant somewhat more requests and a somewhat longer delay before some people with some URLs got the content, but I didn't really care, not when set against the downsides of getting a permanent redirect wrong or needing to change it after all.
In the modern world, I'm not sure how many people will have permanent HTTP redirects cached in their browsers any more. Many people browse in more constrained environments where browsers are throwing things out on a regular basis (ie phones and tablets), browsers have probably gotten at least a bit tired of people complaining about 'this redirect is stuck', and I'm sure that some people have abused that long term cache of permanent redirects to fingerprint their site visitors. On the one hand, this makes the drawback of permanent redirects less important, but on the other hand this makes their advantages smaller.
Today I still use temporary redirects most of the time, even for theoretically permanent things, but I'm not really systematic about it. Now that I've written this out, maybe I will start to be, and just say it's temporary for me for now onward unless there's a compelling reason to use a permanent redirect.
(One reason to use a permanent redirect would be if the old URL has to go away entirely at some point. Then I'd want as a strong as signal as possible that the content really has migrated, even if only some things will notice. Some is better than none, after all.)
Permanent versus temporary redirects when handling extra query parameters on your URLs
In yesterday's entry on what you should do about extra query parameters on your URLs, I said that you should answer with a HTTP redirect to the canonical URL of the page and that I thought this should be a permanent redirect instead of a temporary one for reasons that didn't fit into the entry. Because Aristotle Pagaltzis asked, here is why I think permanent redirects are the right option.
As far as I know, there are two differences in client behavior (including web spider behavior) between permanent HTTP redirects and temporary ones, which is that clients don't cache temporary redirects and don't consider them to change the canonical URL of the resource. If you use permanent redirects, you thus probably make it more likely that web search engines will conclude that your canonical URL really is the canonical URL and they don't need to keep re-checking the other one, at the potential downside of having browsers cache the redirect and never re-check it.
So the question is if you'll ever want to change the redirect or otherwise do something else when you get a request with those extra query parameters. My belief is that this is unlikely. To start with, you're probably not going to reuse other people's commonly used extra query parameters for real query parameters of your own, because other people use them and will likely overwrite your values with theirs.
(In related news, if you were previously using a 's=..' query parameter for your own purposes on URLs that people will share around social media, someone out there has just dumped some pain on top of you. Apparently it may be Twitter instead of my initial suspect of Slack, based on a comment on this entry.)
If you change the canonical URL of the page, you're going to need a redirect for the old canonical URL anyway, so people with the 'extra query parameters' redirect cached in their browser will just get another redirect. They can live with that.
The only remaining situation I can think of where a cached permanent redirection would be a problem would be if you want to change your web setup so that you deliberately react to specific extra query parameters (and possibly their values) by changing your redirects or rendering a different version of your page (without a redirect). This strikes me as an unlikely change for most of my readers to want to make (and I'm not sure how common customizing pages to the apparent traffic source is in general).
(Also, browsers don't cache permanent redirects forever, so you could always turn the permanent redirects into temporary ones for a few months, then start doing the special stuff.)
PS: I don't think most clients do anything much about changing the 'canonical URL' of a resource if the initial request gets a permanent redirect. Even things like syndication feed readers don't necessarily update their idea of your feed's URL if you provide permanent redirects, and web browsers are even less likely to change things like a user's bookmarks. These days, even search engines may more or less ignore it, because people do make mistakes with their permanent redirects.