Claws getting longer is not a good indication of over all health or nutrition.
Poor digestion and metabolism can lead to slow gut- where they do not digest their food properly, quickly or completely. Watch for strange stools or the absence of stool. If he is a young cham, and being fed every day, he should be pooping pretty much every day. Check the stools to make sure they are properly digested; that there are no whole insects in the fecal matter. If he is active and awake, well-hydrated and doing normal cham things, and his bowel movements are fine, you are likely okay. One day of slightly cooler temps is not likely to cause a problem in a healthy adult cham- Madagascar had cool days too- but a series of cool temps could affect a cham, especially one that is growing quickly. Heat stress (either too high or too low) is stress, and if he were my cham I'd be a little careful with him over the next while- limiting handling, etc.
I always keep a spare bulb on hand (several, actually, since I have other herps besides my cham), just in case there is a problem
Keep an eye on your temperatures with a digital probe or heat gun for the next while: new bulbs can burn super hot, depending on the type and brand. I'd be checking the basking and the ambient temps every few hours... but I'm a bit of a worrywort!