ATS blowing warm air at idle and I’m melting in this Sharjah heat

My 2015 Cadillac ATS has been pretty solid since I got it last year but now that the weather is starting to turn properly hot again I’ve noticed the AC just gives up and starts blowing lukewarm air whenever I’m stuck at a signal for more than thirty seconds, and the moment I start moving again it cools right back down which is doing absolutely nothing for my mood during the afternoon school run when I’m sitting in traffic on Al Ittihad Road sweating through my shirt while the kids in the back keep asking why it’s so hot. I’m pretty sure it’s either the cooling fan not kicking in properly at low speeds or maybe the compressor is just getting tired after nearly a decade of UAE summers but I’m not about to start throwing parts at it without someone who actually knows Cadillacs taking a proper look, and I’ve been trying to find Cadillac AC Workshop Experts in Sharjah that won’t just tell me I need a whole new system when it might just be a fan module or a simple regas with the right amount of PAG oil. Has anyone had this exact issue on their ATS or CTS and actually got it fixed without a second mortgage, because I’d rather not spend the next five months arriving everywhere looking like I just ran a marathon.