I renewed my enhanced driver's license. However, it has not arrived yet, and I’m supposed to drive to Canada tomorrow. If I have my old enhanced license with a temporary one attached to it, plus a birth certificate, will I be able to get in and out of Canada?
You are probably good to go, though you might be harassed a bit more than usual.
For the trip into Canada across the land border what is required of a US citizen is proof of citizenship and a photo ID identifying you as that citizen. Your birth certificate and the (expired) enhanced driver's license provide evidence of your citizenship, while the temporary license and (expired) enhanced driver's license associate your face with your name. If you happen to have any other photo ID you could carry that too for extra insurance, but what you have should be sufficient.
The trip back to the US may be more of a problem since you are required by regulation to have a WHTI document to reenter the US by land, which your enhanced driver's license is except it is expired (or was cancelled?). The saving grace is that they cannot deny entry to a bona fide US citizen and there is no particular penalty for not having a valid WHTI document, so if the primary inspection is unwilling to accept the expired EDL and the temporary DL (showing that the renewal is in the mail) as meeting the requirement the worst that can happen is that they'll send you inside to secondary to "investigate" your citizenship. This may take some time and they may give you crap for traveling like that, but ultimately they'll let you go home.
This isn't perfect but if you need to travel you should be okay in both directions.