Hi and welcome to the forum.
You will have guessed from previous posts that there is a bit of an urgent problem to do with your stocking.
To put it briefly, it takes time for a tank to build up a colony of bacteria big enough to handle the fish waste, so you cannot add a whole load of fish all at once.
Also, you would be heavily overstocked for a 10 gallon tank even if it was mature and had developed its full bacterial potential.
What you need to do now is one of two options:
either take all the fish back to the shop and do a fishless cycle (pinned topic). If the shop knew that all these fish were to go in a new 10 gallon- give them an earful. If they were not fully aware of the facts, you will have to be a bit more tactful.
or, take back all the fish except two female guppies or one of the orange fish (assuming they are platies), then buy a test kit, keep testing every day for ammonia and nitrites and do a partial water change whenever either goes over 0.5 ppm
as for your question: new water added at a water change shouldn't be warmer than the water already in the tank, so that shouldn't send them into shock. Mix it up in a bucket first to get the temperature right. And don't forget to dechlorinate.
and just one more point: from now on, never buy a fish until you know its name and have looked up its requirements either in a good book or online. Fish have very different requirements: some grow massively big and need monster tanks, some are aggressive, others need to live in groups, and they don't all eat the same things. Buying a fish is like buying a mammal- you really do need to know if you are getting a hamster or an elephant!