Lots of people report Mac heats up and fans come on when using Lightroom. I believe this is a normal situation, and you should search the forum for other similar reports.
You haven't told us what version of Lightroom you were using, and what version you have updated to. I WANT THE VERSION NUMBERS and not words like "most recent".
Same question for the operating system.
Have you changed the type or amount of editing you are doing? Are you doing lots of brushing and/or spot healing? Have the photos you are editing changed (new camera, or different quality setting, or switched from JPG to RAW)?
Lightroom CC 2015.10.1 - updated on June 1st
MacOS Sierra 10.12.5 - updated on May 20th
I noticed it started heating up in the last days, so my inclination is to say it was the update to LightRoom that did it.
I've been working on this project daily for the past year.
I haven't changed anything in the way I work, the images, etc.
The editing I am doing in Develop mode is not heavy - mostly exposure and temperature. Sometimes lens correction. Even less brushing. No spot healing.
It used to overheat when I first installed LightRoom.
I can't quite remember what I did then... it might have been an update.
And optimizing performance - maybe with the previews.
by the way, it only happens when I'm in develop mode.
Your computer isn't "overheating", it is behaving normally. The number one complaint about LR has long been that it is too slow, and Adobe has worked hard to make sure it uses as much of your CPU and GPU as possible. Most applications use only a fraction of the CPU and GPU, but when an application heavily utilizes them, the Macbook will run hot and turn on the fans, which is by design: About fans and fan noise in your Mac - Apple Support