I have seen people keeping caladiums as houseplants, so I brought mine indoors well before frost. A few weeks later, it died back, so I gave up on that plan! It's been sitting in a cool dark spot for a few months now and I'm hoping it will come back to life.
What is the best way to get it going again, I'm specifically wondering if it will do better with more heat.

When the weather starts to warm up again, put the pot back outside and water it.

Caladiums loves humid heat. That has been the drawback on my side..we get too much dry heat during the long dry months..so got to have them on the brightest side of the garden from mid Spring to Fall, but not under our direct sun. And once awake, got to keep them well watered.

Winter is doldrums time..so it all depends on your outside environment if it is suitably warm enough later in Spring. I usually bring out my overwintered plants when overnight temps show 50F and higher. With Caladiums, may need higher..70F and higher.

If I'm remembering right, @skylark keeps Caladiums in pots, perennially.

Yep, the larger the tubers the longer you can overwinter them. They need a few months rest no matter what temps. I keep them dry in pots and when I see little shoots starting to appear I lift them out, clean them up (small ones can dry rot easily and don't survive well) and then I usually put them in very moist sphag on a heat pad to sprout roots and then I pot them up and they sprout leaves in sunny window in NJ in April-May. They need temps at the roots to be above 65f at all times. But 70-80f is better for growth, so I don't put them outside until mid-June usually.
I am wintering in So FL so I decided to experiment and brought them over and they did not decline insep-Oct as usual , but around mid Jan, as the pots were outside and temp were 80/65-70F until then. I think that brighter light levels and higher temp with higher humidity all helped them to decline much later. They woke up in March and by April were going strong outside (but mar is already 80f here). So this past year instead of 6 mo in NJ they grew for almost 10 (with summer in NJ and then back to FL👍😁).

How long they go depends on a cultivar.
Some sprout/decline early (like 'Red Flash'), but my Mrs H alderman' is super slow until Jul and it actually kept some leaves thru the winter in So Fl (I don't let it cool below 65f, bring it indoors for a few weeks). My 'White Queen' needs beauty rest and 'Red Flash' is almost a sleeping beauty ..it grows furiously for 4 mo and then just gives up.

So I think that with bottom heat and supplemental lights up north and at least 50% humidity you can make them go a few extra months. My guess why yours declined in the fall indoors is that roots got chilled outside at night and then lower light levels indoors added to decline.
The tubers can rot easily when cool and damp and then dry rot can set in in the dry pot too. I would say if half of tubers survive it's good enough. So give it a try.

Thanks for all the info, especially the temperature details. I probably let it get too cool in fall to remain active. I don't necessarily want to keep it as a houseplant but storing dormant hasn't worked for me in the past.

I pulled mine out of the pot just to see if the corm was in good condition. It is! Of course I didn't pay attention to how deep it was, and might even have gotten it repotted upside down, so fingers crossed. So I should wait till it sprouts to provide light and heat?

Do you mean spaghnum peat or long fiber spag ?

I plant mine shallow not more then 1/2", so that when they wake up they shoot little sprouts out of the soil that are pink. They will do it even in totally dry mix.
When you dug them up you should have noticed sharp tips on corms: that's the up side. The bottoms are flat, they sort of flake of dry in spring and you should see light colored firm bottom, not soft not brown.
They sprout roots from the top of the corm , so once they have started they need like an inch or so of mix above them to keep the roots moist for the rest of the season (as the top dries up fast). I then sprinkle more mix on top if I see that they are too shallow.
I don't dig them up every year: they will dry up too much if stored dry. So they recommend to put them in dry peat until spring. It's too much to bother for me.
If they don't have pink tips you should put them back in pots for now: it's too early to start them up. I'd say March at the earliest unless you are in Deep South.
So my big ones i usually start up on heat mat in clam shell in moist long fiber NZ sphag all covered up loosely. And you then need to carefully remove sphag for planting as the roots might break.
This is the pic of my corms sprouting : roots from LF sphag , ready to be planted:



The rest (in pots ) I start up by just watering lightly to moisten the mix a bit and keeping them in the sunny window to heat thru. They will take at least 4 weeks to wake up and show some signs above the surface:pink tips.
Then you can start watering slightly more until they grow a first leaf , then water a bit more still. It is sort of like starting Callas or Amaryllis.