I've seen it done before. They were put together in the same tank (5 bowfin and 3 SH's) when they were all around 3-5 inches. The SH's were actually a bit bigger than the bowfin when first introduced. They swim and school together like they can't even recognize there are differences from each other now. I do not however, know what would happen if the constant food supply stopped and hunger was allowed to set in. If they're young there's a good chance they'll be fine. VERY similar species, remarkable that they aren't even related.
i think theyd be ok as they almost look like each other it could be a super good thing or a super bad thing it all depends on THEM and there personalities =D
Both fish are fully capable of acclimating to different temperatures of water. I've seen big old bowfin living in tropical tanks and anyone in the US knows that Snakeheads can handle the cold... it's one reason we can't have them. Just make sure the bowfins aren't too small if you're putting them in warm water.