One step up from CR 1/3 is CR 1/2
There are a couple ways to santiy check this. First of all, these two CR's respectively award 135 and 200 XP for defeating the monster. This XP difference makes sense for a +1 CR difference; a 30-50% increase.
Second of all, you can check table 1-1 in the bestiary to see whether the resulting creature makes sense at its new CR. Do his attributes better match the CR 1/2 guidelines, or the CR 1 guidelines?
I suspect if you're upgrading a CR 1/3 creature, it probably has a single non-maximized hit die, and between 5-7 hit points. A +1 CR template is unlikely to add hit dice, so at very most you're looking at an extra 1 or 2 HP from a higher constitution score. Bottom line, this creature probably has below-average HP for CR 1/2, which means it's very unlikely to be strong enough to merit a CR 1 designation.