Hot Water Temperature Varies

Depends on what was done before you had your shower.
If you did a couple of loads of wash or followed someone else who showered, your water heater is just not keeping up with the demand.
How old is it?

Outside water temperature. The shower mixes "cold" water from outside the house with hot water from your water heater. The hot water is around 120 deg F and is controlled by a thermostat. The outside water is whatever it is. When I was growing up in the deep South, the outside water temperature in the summer was 80+ degrees. I just needed to crack open the hot water to get good bath temperature. In the winter, outside water temperature would drop to the 50's so much more hot water was needed.

As noted in the previous post, if your hot water heater is cold because you've used up all the hot water or because the thermostat is off, that is another issue.

I don't think seasonal changes can account for daily differences like these, Engineer. My first guess is a faulty thermostat but I've never seen a thermostat do this. My next guess, poltergeists.

That's just the way they work, msmarg. Maintaining a constant temperature would be more complex and more expensive. Rather than heating the water continuously, the gas or electric comes on a a preset point, and continues to heat it till the high temperature limit is reached.

If you run a bit of hot water before showering, it should kick in, and give you a nice hot shower.

I don't think that's quite right, Roger. Water is heated to the temperature that the thermostat is set at, I believe the factory setting is around 140 degrees F. If there has been no pull on the hot side for a period of time, the entire tank volume will be heated pretty close to the set thermostat temperature.

A water heater never heats to the hi-limit point unless there's a malfunction at the junction. Then the pressure-temperature relief valve opens and some pretty scary stuff blasts out.