If so, what is it called?

We have a small section of our basement that gets 3-4 inches of standing water when we have very heavy rains (2-3x/year at most). Obviously we could put a sump pump in, but the previous owner successfully addressed water in the rest of the basement with a new drainage system (and then we bought the house before the first rainy season, so they hadn't been able to test its efficacy), so we have been working on the system of french drains outside this small area to try to adjust the trenches to stop the water. So---we would prefer not to dig into the foundation for a sump pump if, in theory, we'll soon successfully get the drainage right and would no longer need it. (Challenge is that it's only tested a couple times a year, so we have to wait a season to see how effective our tweaks are!)

But---we just moved our furnace into the small room with water issues (long story, but on balance a better place for the furnace). It's on a platform that should put it above the water line even when we do get water there, but we want a backup system in place until the drainage is 100% squared away.

Is there such a thing as a temporary pump that would work like a sump pump (be plugged in and ready to go, be automatically triggered, and be effective enough without the deep basin)? Are there other good mobile or inexpensive solutions for moderate, occasional water problems? (We do have some notice since the flooding is only with heavy rains at the end of a long period of rain, so it could also be something that would get put in place in advance.)

Would love any ideas, as we want to be sure we don't fry the new furnace! We have about another month before the first rains of the season are likely to start, so not a huge amount of time. Thanks!