Unlikely. The following is a brief summary why.
Brains use up a lot of energy. Broadly speaking, animals have evolved to have a brain size sufficient to do the task at hand, but no more. Occasionally evolution has caused the brain to shrink compared to an ancestor (eg Australian Koala, which has something of a split brain). Very few animals use tools, but those that do, need bigger brains than other animals. Certain primates use tools, as did our ancestors.
An ancestor to humans (homo erectus from memory) was the first animal that used fire as a tool. This was a crucial step, and set a chain effect in motion. The disadvantage is that fire is such a complicated tool, it needed a bigger brain. The massive advantage is that it allowed homo erectus to cook meat and other food, making food safe to eat, and making it easier to digest. (Cooked meat requires around 30% less energy to digest than raw meat, even in a species not used to cooked meat, as some documentary I saw, demonstrated.)
Once our brains became more capable, our ancestors found other things to use them for, and obtained further advantages over the rest of the animal kingdom. This in turn gave bigger brained smarter beings an advantage over others, etc.
I can't see another species achieving that unless humans die out, and another species evolving enough to be able to use fire as a tool.