Should be no temperature difference between ceramic and porcelain tiles. As far as it being cold, a little research on your part would have revealed this. This is why it's important to research decisions you have to live with for years. At least you'll be happy in hotter weather.
Often the sand on the surface of the newly dried grout will release some with the first sweeping. There should only be a tiny bit of sand with this first sweeping, and once the bit of loose surface sand releases, that should be it.
Scratch the grout with your fingernail. It should not budge at all. Then scratch it with something plastic like a plastic fork or spoon. It still should not come apart. In 3 days it should be hard and in 7 days should be very hard.
If it is coming apart at all with your fingernail, you're screwed.
If it is a crappy job but you have to scratch at it pretty hard with a plastic utensil to make it come apart, you have a bad job but could salvage it some by applying a quality grout sealer. The sealer normally just waterproofs it, but in your case the sealer soaking in could make the surface hard enough for you to live with the bad job. If you have dogs, their toenails will destroy it.
P.S. grout sealing is optional. Most people are willing to do it themselves rather than pay to have it done. If you wanted it sealed you should have told the installer in advance. Quality modern grouts with polymer are very stain resistant as-is, so I don't like to apply sealer unless I'm requested to.
Let us know what you find.
thetiler