Normal ricotta doesn't, but the "ricotta recipe" that I gave SlowRain does.
Basically you take normal milk that you would use for cheesemaking and heat it to 42 C. You dissolve 4-6 grams of citric acid in water and slowly add that solution a little bit at a time to the milk while stirring *slowly*. I forgot to mention that you probably don't need all of the acid solution! (Sorry, SlowRain!) Then you drain. The trick here is that at 42 C, milk coagulates by acid at a pH of 5.1: which is just perfect for melting (and I think it actually rebounds a bit as the calcium phosphate in the curd is liberated -- so after a day or so, the pH will probably be 5.2 or so. But I don't have a pH meter to verify this). Since the milk is never raised to a high temperature, the proteins never denature and so the resultant cheese will melt. Unfortunately it doesn't stretch very well because acid formed curds are too delicate. If you try, it leaks fat like crazy.
Now, the cool thing about this is that if you tweak this recipe *just a bit* you can make a cheese you can age (which I call "Mistem cheese", but whose proper name I have discovered is queso secco). Basically do exactly the same thing but after you heat the milk, add about 1.5% of the total volume of milk as yogurt (i.e. for each litre of milk, you add 15 grams of live yogurt). Hold the temp for 1 hour to ripen the milk and develop flavour. Then make your curds.
Try to consolidate the curds as best you can and transfer them to a cheese cloth lined basket (you can just use a collander or whatever you want for a basket). Best to soak the cheese cloth in the whey before you line the basket so that the cheese doesn't stick to it. Fold the cloth over the top of the curds and put a bamboo mat on top of that. Immediately flip the cheese so that the bamboo mat is on the bottom and the basket is on the top. Try to do this reasonably fast: so you've put the curds in the basket and you flip it within 5 minute. This is because the curds are hot and they will form a skin that later won't stick to things. If you wait too long, it won't form the skin. Wait 15 minutes and flip again, so that the basket is on the bottom. Wait 30 minutes and flip again (bamboo mat on the bottom now). Wait an hour and flip again. Wait another hour and flip again. Take a look at the cheese and decide if you think it needs another hour or if it is solid enough (it won't be totally closed, without cracks, but it can get pretty close).
After 3 to 4 hours of flipping, dry salt the cheese. Weigh the cheese (it will be about 150 grams per litre of milk you used -- ironically more if you use homogenised milk). Measure about 1.25% of the weight of the cheese in non-iodised salt (i.e. sea salt) (or about 1.8 - 2.0 grams per litre of milk you used). Rub the salt all over the cheese and then let it sit for an hour. Then do it again (i.e. 2 applications of the same amount of salt separated by 1 hour). Let the cheese drain for another hour.
Get a plastic tupperware style box that your cheese will fit into and is about 3 times the volume of your cheese. This will be about 500 ml per litre of milk that you originally used. So if you used 2 litres of milk and made a 300 gram cheese, the box should hold a volume of about 1 litre. (The size is not super crucial for this cheese, so just try to find something approximate). Cut a bamboo mat to fit the box (pro tip: don't cut the strings ;-) ). Boil the bamboo mat and sterilise the box somehow. Put the bamboo mat in the box, put the cheese on top of that and close the lid. Put the whole thing in your normal fridge.
Every day, flip the cheese and wipe out the box. If you get mold, wipe it off with a brine solution containing a bit of vinegar. This cheese has no rind and so when you wipe the cheese, the outside will kind of dissolve. This is not bad: the stuff that your wipe around will fill up the cracks, a bit like making a stilton cheese. If you wipe it fairly regularly (say once a week), you will have no cracks on the outside. This cheese is always really dense as well, so you will have virtually no mechanical holes in the centre.
You can eat the cheese within a week as a fresh cheese (in which case I believe it is called a queso blanco), or you can age it for up to several months (when it is called a queso secco). The longest I ever aged it was 3 months and it was really, really good. The cheese also melts fairly nicely and you can use it on potatoes or whatever (I don't think it would make a very good grilled cheese, though, because the cheese doesn't stretch).
I made this type of cheese for a year before I ever got into making rennet cheeses. It also makes an *amazing* blue cheese (though it doesn't get veins because the paste is too dense -- don't try to piece it because the cheese will just crumble on you). Rennet cheeses are way more versatile, but if you don't have access to rennet this is a really great way to go (and you develop a lot of normal cheese making skills along the way).