How long is the term for a pro tempore moderator?
The term is "until the graduation election".
Pro-tem mods are added when needs exceed current capacity. This can be a straight-up addition, when the workload grows beyond what the original three moderators can handle; this happened on IPS, Genealogy & Family, Worldbuilding, and Christianity, to name a few. Or it can be because an existing pro-tem stepped down, which is how I got two of my pro-tem diamonds (Writing and Beer, Wine, & Spirits).
If you feel your site needs more moderators, bring it up on your site -- though usually your existing moderators would lead the charge there. If you feel your site needs different moderators -- that is, if you are unhappy with one or more of your current pro-tem mods -- then you need to raise the matter with SE, who appoints pro-tems. Use the "contact us" link at the bottom of every page. Removal of moderators is very, very rare, done only in the case of severe problems. If you just don't like someone, you are unlikely to be successful.
While this post is mostly about removing elected moderators, you might find it helpful for understanding general philosophy and policy.
Another possibility is when the existing pro-tem moderators cannot handle the workload, which might happen on sites about
controversial subjects subjects where people have a lot of controversial opinions about. In that case, new forces can be called in; this recently happened on Interpersonal Skills. You can compare the difference between the current moderator team and the original three.