I think this would be a great (and very tasty) science fair project. As you probably know, regular ice cream melts because it contains a lot of water. Water is a solid below 0 degrees Celsius (32 degrees Fahrenheit) and a liquid above it. The melting point can be changed a little bit by adding things (like sugar, salt, or milk proteins in ice cream), which is why ice cream might not melt at exactly 0 degrees. But "hot ice cream" is a very different material. The reason it solidifies is not because the water stays frozen, but because of a special ingredient: methyl cellulose. At low temperatures, water molecules like to stick to the molecules of methyl cellulose. But at high temperatures, the water molecules jiggle around a lot more and can no longer stick to the methyl cellulose. When this happens, some of the methyl cellulose molecules stick to each other instead, and this makes the mixture take on a gel-like consistency (the process is called "thermogelation," meaning that temperature controls the process of forming a gel.)

Now, to answer your question about melting point: it is kind of confusing to try to define a melting point for hot ice cream, since the "melting" (thermogelation) transition happens in the opposite direction from a normal melting transition! Hot ice cream will be a liquid (melted) at low temperature, and will solidify as the temperature is increased. The transition temperature, technically called the gelling temperature, is around 50-70 degrees Celsius (approximately 120 - 160 degrees Fahrenheit.)

A mixture of methyl cellulose and water will have some interesting properties, but it will not taste very good, and certainly isn't ice cream! That is were the other ingredients (yogurt, cream cheese, flavors) come in. I'm sure there are a huge number of recipes to make "hot ice cream" using methyl cellulose and various dairy products. However, when experimenting with chemistry and cooking, it is good to start from a recipe that you know for sure will work (for instance, one of the recipes at the links you provided), and then make only small changes. One thing that is probably safe to change: the flavor! As long as the amount of liquid you add is about the same, you could try different flavors: maple syrup, chocolate syrup, honey, vanilla, fruit jam, etc.

I suspect the amount of methyl cellulose relative to the amount of other ingredients is very important: if you decrease the amount of methyl cellulose, the ice cream might not be solid enough. In fact, this is something you could test in a science fair project- how does increasing or decreasing the methyl cellulose content affect the ice cream?

Here is a recipe similar to the ones you linked to, with a little bit of explanation of the science: hot ice cream

Here is another recipe for methyl cellulose ice cream that uses heavy cream and milk instead of yogurt and cream cheese (this one is coffee flavored but you can change that): methyl cellulose ice cream

By the way, methyl cellulose is sometimes called Methocel food gum. It is safe to eat, but it can give you a stomachache if you eat too much of it!

Since the frozen part of ice cream is actually the water constituent of the cream, you may have read that it is quite easy to LOWER the melting point of ice cream. A solute added to water tends to inhibit its ability to solidify and necessitate lower temperatures for freezing. Salt water and alcohol in water are good examples of this. The exact freezing point of course depends on the concentration of solute (e.g. NaCl or ethanol) in the water. To RAISE the melting point of ice cream, as you say, is a bit trickier, and the recipes you found use the polymer methyl cellulose, which is not soluble in water above about 50 degrees Celsius (122 degrees Fahrenheit). Technically, the melting point of the ice cream mixture is not changed, rather it is the solid precipitation of this polymer that makes the ice cream solid at higher temperatures. As far as other ways to make hot ice cream, a polymer with limited aqueous solubility is a promising solution, though you might imagine it is difficult to find such a polymer that is also safe to eat. This is probably the reason you haven't seen another method for preparing hot ice cream.

Polymer-based solutions to raising the melting point of ice cream are chemically the most likely to succeed, though the ice cream may start to resemble butter, since saturated fats (such as those that make up most of the fat in butter) tend to have higher melting points. Good luck!

You're asking two things:
1. How can you raise the melting point of ice cream to a temp that’s still cold but less cold than normal ice cream? Stabilizers is the answer there: stabilizers for ice cream and you can buy them at Modernist Pantry and other sites, e.g. for ice cream stabilizers.

2. Can you make hot ice cream? The cookbook Modernist Cuisine writes (page 4.127) “one of the quests of Modernist cuisine is to develop the fabled ‘hot ice cream’ dish, a goal that has so far eluded eminent chefs. You can use methyl cellulose [which melts as it cools, unlike most thickeners which set as they cool] to make something like hot ice cream, but to many tasters the dish lacks a true ice-cream-like texture and instead resembles an odd, dumpling-like object that melts as it cools.”