According to SRD:
A swarm is immune to any spell or effect that targets a specific number of creatures (including single target spells such as disintegration), with the exception of effects affecting the mind (charms, compulsions, morale effects, patterns and fantasies) if the swarm has an intelligence score and a hive spirit.
Demoralizing an opponent in itself would not work because it is an effect that targets a single opponent and Rat Swarm does not have the Hive Mind feature.
The invocation of blistering affects 30 feet. radius, thus exceeding the limit, as a specific time.
Unfortunately, this also changes in general "verbal threats and demonstrations of prowess" from intimidation to very specific "insulting tirade" and the spell has a language dependent descriptor. Normally, no language is listed in rats. This spell will not work, unless you can make them understand first.