It has flavor, but its consistency is too thin. Will letting sit over medium low heat evaporate enough to increase its density or is this useless? Would bringing it to a boil help more. I don't want to ruin its flavor and am afraid bringing it to a boil with high heat will do just that.
Yes, cooking it more to evaporate off some of the liquid will definitely help. This is called reducing a sauce. A moderate simmer would be the appropriate temperature. You want to see occasional bubbles but definitely not a rolling boil. Stir it occasionally, making sure to get the bottom of the pot to avoid any scorching. It is possible to have it be quite liquid on top and rather dense in pockets on the bottom, which can then get well above 212 F and reaching the point of burning.
There are a few things you can do to thicken your sauce:
- Simmer - you can simmer the sauce at a low heat for quite a long time without affecting the flavour (generally improves it). Many Bolognese sauces are simmered for 30+ minutes.
- Thicken - add 1-2 tbsp of corn starch (or flour tempered). Many commercial sauces do this.
- Add paste - add a small tin of tomato paste (in addition to either of the above). Adds both flavour and thickening mojo.
Contra the previous answers: when using fresh tomatoes, one key to avoiding watery tomato sauce (and sauces based on many other kinds of vegetable purees) is to bring to close to a boil quickly at the start.
Fresh tomatoes contain natural enzymes which will break down pectin and other other thickening components. By heating rapidly to a boil (or nearly so) at first, you will deactivate these enzymes. Then reduce to a low simmer to preserve flavor components during the remainder of cooking. If you don't do this first step, the sauce will turn watery and you'll spend a much longer time thickening it again by reduction (or other means).
For more details see Kenji Lopez-Alt's Q&A here (where he quotes Harold McGee's similar advice on the same topic).
(Note that this advice only applies to sauce made from fresh tomatoes. Canned tomatoes have already been heated in the canning process, so the enzymes should already be deactivated. Canned tomatoes can just be simmered slowly.)
Beware of hard boiling tomato sauce. Once it starts to thicken it'll burn to the bottom of the pot if not stirred every few minutes. That'll impart a 'Carbon-ara' taste that most people don't like. Dried mushrooms, Shiitake or other, such as you can get cheaply in asian food stores, make an excellent thickening agent for tomato sauces. They hydrate in 10 minutes or so when boiled, and suck up a lot of water in the process. If you don't want chunks of mushroom in your sauce, the dried material can be powdered in a coffee grinder before adding to the tomatoes.
- A large (.25 lb) parmesan cheese rind
- bring to a boil first and then reduce to a simmer.
- expect no less than 4 hours.
- A deep kettle is better to reduce the chance of scorching because of too much surface area with a shallow pan.
Note: The above is the Italian (Luca) way and guarantees a thick fresh tomato sauce.
Definitely simmering longer will help the sauce. I agree with previous answer that you should bring it to boil and then turn down the heat to simmer. I've made both fresh whole tomatoes and canned. Another thing that I've noticed is that using the right pan is HUGHLY helpful. A wide shallow pan will do much better than a deep pot.
There is good advice here already but another situation people may run into is getting a watery sauce when using whole canned tomatoes, e.g. San Marzano's. I prefer to not blend my sauces. If that it the case with other readers here remember that you really need to break the tomatoes up with a flat edged wooden spoon/spatula or some masher in the pot throughout the cook. It'll help release the water that builds up after you kill the heat as the pulp relaxes and squeezes water out.