Heat and water safe material for internal dishwasher repair
The recommended, long term method
There are quite a number of places on line that sell repair parts for all types of home appliances.
It will likely be easier to purchase and install the proper replacement part than to attempt to repair a part.
Using your favorite internet search engine, look for

replacement parts &lt;make&gt; &lt;model&gt;

Where &lt;make&gt; = Whirlpool, or GE, or Bosch (as appropriate), and &lt;model&gt; = xyz, or pdq, or alpha123soup-b as listed on your machine.
and you'll probably come up with 4* options right off the bat!
*number guaranteed to be correct for as long as it took me to type it.

The short-term quick fix methods
Since the OP has indicated that he's looking for a short-term repair before replacing the appliance...
All the big-box home improvement stores stock all sorts of miracle leak stopping tapes and wraps that will work on anything from glass to plastic to metal to cement and more!!! (As seen on TV!™) You could probably even pick some up at your local 24-hour superstore while you're getting groceries.
It seems like this would be a good time to try one out and see how close it comes to the claims on its package. If one doesn't work very well, try a different brand. I've never had need to use any, so couldn't make a recommendation.
If you wanted to be really solid, but spend a bit more money (or maybe not), and can get that pipe out of there, a rubber coupling (sometimes known as Fernco connector) should be more than sturdy enough to hold in the pressure and, for only a couple of years the rubber should take the heat, as well. It might not last much beyond 2 years, but that's all your looking for.