Kitty is lethargic. Pup is drooling. Kitty won't eat her favorite dinner. You left pup in a very warm room and maybe it was too warm.
Is this serious? Is this going to pass or do I need to contact my vet? Or do I need to get her to her vet pronto?
Shock is the underlying issue with any injury. In shock, the circulatory system is starting to shut down. There is a simple test to tell if your petis in shock, moving into shock or coming out of shock. It is called "Capillary Refill" or CRT (Capillary Refill Time).
Very easy to do. You press your finger against your pet's gums to produce a blanched (white) spot and then measure the time it takes to return to pink. In a healthy animal it will return to robust color in under 2 seconds, indicating that their circulatory system is pumping properly. Barring other issues, you can likely handle the emergency on your own, perhaps with a phone call to your vet or one of the emergency vets for some coaching.
Recheck CRT periodically until your pet returns to full normal. Shock is the underlying "must avoid" at all times. When in doubt, check and recheck cap refill, CRT, to see how your pet is progressing and be prepared for a call and a trip to the vet if it goes over 2 seconds.
Please note that CRT is a quick measure of circulatory function, something that is most often affected by trauma. There are disease states that can exist with normal CRT.
Here's a great YouTube not just on cap refill but on all your pet's basic vital signs.