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