404s generally do not cause problems with SEO unless you constantly have them! Search engines gauge stability in a large number of ways and constant 404's will degrade your stability score if and when the 404s are created by you and not externally. Sure a few here and there is no big deal, but as a rule, I would avoid it.
Here are a few points to consider:
Scenario 1] You have a temporary page that you then delete. You have the following situation:
1.a] You may have a page in a search engine that directs users to a page that does not exist. This is bad for user experience (UX). The user is disappointed and may not give you another chance.
1.b] Someone may have shared the page using social media. Same thing. Bad UX.
1.c] Someone may have linked to that page. More UX.
1.d] If you have an e-commerce site, shopping site scraper sites may have picked up on your offer. Potential problem.
You can place a 301 redirect to another product page where this makes sense to do to recover UX and can be advised. However, this does not seem to fit your scenario.
Besides the UX problem, you will likely experience an increase in your bounce rate as a result. It may be minor in your case. You decide. However, I would think that UX and bounce rates are enough of a reason not to create these temporary pages.
Scenario 2] You are constantly adding and removing pages. Besides the problems listed above, you now have another problem.
Search engines are constantly measuring sites for stability which is a part of the sites trust metrics. Part of that measure are server errors. Some level of errors are easily forgivable since they do happen from time to time, however, constant or significant errors does, in fact, degrade a sites stability score. This is a bit of a fuzzy area. Yes, Matt Cutts says on one hand that a 404 is best under different scenarios. He is right. Google generally advises that if a page is gone that a 404 exist except where UX is desired to direct a user to a similar product. But you have to listen to what Matt says very carefully.
In the video linked in another answer, Matt does not say that 404 errors do not effect SEO. He says nothing of the kind. He does say two important things however if you are paying attention. The first is that it is a matter of scale. Let me explain. A large site that generates a number if 404's is to be expected whereas a smaller site with a disproportionate number of 404's can be an indication of site quality. This holds true for other errors too. The second thing Matt says is use the available after meta-link if it applies. This is a good idea. Here is the Google page on that: http://googleblog.blogspot.com/2007/07/robots-exclusion-protocol-now-with-even.html This may be a solution for you. In this case, Google will drop the page from the index on the appropriate date. But that is Google. What about Bing and others? I am not sure. You can search for an answer on that.
Some number of 404 errors are to be expected as a site changes over time. That is a given and they do not effect rank at all. However, as I said before, a higher number of site errors is an issue and will effect SERP placement. This is well known. If you doubt me, you can test this yourself by creating a fair number of errors. Your search traffic will drop for a period even after the errors are fixed to begin returning almost 60 days later. Even then, it can take longer. While 404 errors are different in that they are a part of doing business on the web, a disproportionate number of them will effect SERP placement. I had the opportunity to test this for myself last year knowing full well what would happen. I removed 184,000 pages from my site overnight. SERP placements for all pages dropped significantly for a good period of time despite the many hundreds of thousands of other pages on the site.
I would use a "specials" or "limited offer" page that you reuse. This does double duty for you. If you always have specials or limited offers, then this page will be fresh and should perform rather well if you do your SEO homework well. If this does not fit your scenario, then I would advise using the available after meta-tag. It has been around since 2007.
