Sorry to hear about your dog.
There are a lot of possibilites for his change in behavior.
He could be anemic (low red blood cell count), which would make him feel very tired. If you look at his gums, are they pink in color, or are they pale? If pale, he could be anemic.
He could have liver disease, kidney disease, an infection, cancer (I hope not, but he is an age to worry about it), or a hormone imbaXXXXX XXXXXke Addison's disease (under active adrenal glands).
So there are a lot of possibilities. The place I would start is with a good physical exam. Just examining him will rule some things out, like anemia.
His gums are pink
That is good.
But he still could have any of a dozen conditions that would cause a 10 year old dog to be overly tired, and not eat like normal.
Is he drinking water? More, or less, that he used to?
He seems to be drinking less water
If he had kidney disease, he would probably drink more, so this is probably not kidney disease.
But that leave hormone imbalance, liver problems, infection, parasites, or cancer as possibilities.
At his age, I would be worried about him, especially if he is losing weight.
By eating less, he is telling you the only way he can that he feels weak, tired, sick. His appetite is a good measurement of how he feels.
How long should I leave him go like this before I take him to a vet. This is the 3rd day he is like this.
I would not wait much longer. Dogs just don't stop eating normally, unless there is a reason. The sooner you find out what is wrong, and the earlier you catch it, the more options you will have.
Can you take his temperature with a rectal thermometer? Normal is between 101 and 102F
Is it true that when a dogs nose is dry or warm they have a temperature
No. You can't tell temperature, or anything, by the nose.
No idea where that got started.
It should be moist, but in my dry climate I see a lot of healthy dogs with dry noses.
If he has a fever, his ears or armpits may feel warm, but you really can't tell without a thermometer.
We are in Fl now for the winter so I don't think that is the case but he does have a dry wam nose right now
He could have a fever. But a fever is only a sign of illness, not a disease. If he has a fever, all the more reason to get him checked out.