Baby wipes, not napkins. They clean spills, faces, and the dashboard crime scene. Compact jumper pack, cheap blanket, and a real phone charger that stays in the car. Toss a couple shelf-stable snacks so the meltdown timer resets.
I get this every winter in my shop. Cold batteries act full on the bench then fall on their face the second the bit bites. Bringing the packs inside overnight, charging them warm, and only snapping one into the drill when I am ready fixed most of it so yeah... i give the trigger a quick no load blip to warm the cells and keep the drill in low gear for screws. Works great.
If it still tanks when warm, look for extra drag. Pull the bit and run it slow while you listen and feel. Smooth sound and a long coast down points to a healthy gearbox. Harsh sound, short coast, or a whiff of hot smell points to added load. You can clean the chuck and blow out the front, and a tiny drop of light oil on the jaws can help if they are sticky. Avoid charging a cold pack. Let it warm to room temp then charge. Do one or two gentle discharge and recharge cycles to refresh the gauge. If a friend's warm battery runs your drill fine you have your answer, and if not then the tool likely needs attention.