Okay well I am not 100% familiar with Jacksons but they do need that temp drop regardless. Now Jacksons chameleons are from africa and some in the mountains where it is up high and the temp drops dramatically at night. I would think that as long as it doesn't get below 50 degrees in your house he should be fine even without an emitter. I do know that Veiled chameleons(who require more heat than a Jacksons) can withstand a drop of down to almost 50 degrees.