Yes, you don't need a heater.
Goldfish are cold water fish and prefer it to be that way. It may interest you to know that in very warm temperatures black moors are notorious to change their velvety black color to orange, and you may not want that. It will not in the least hurt your fish to add an airstone (I think that's what you mean by pump...the pump is the thing that you plug in that pushes the air through). With so many fish in such a small space, it will help to promote the exchange of oxygen exchange at the surface of the water. If you aren't right now, you have to cycle your tank. You can find several articles written on the subject if you search through past topics, or simply research it on a search engine.
If you cycle your tank and do large regular water changes, your fish should be ok for a temporary ammount of time. However, if you really care about your goldfish, you should really consider getting them a larger tank. You see, goldfish are messy fish. They poop A LOT. They also excrete large ammounts of ammonia out from their gills. Ammonia, in even teeny tiny measures, will kill your fish. This means that your fish will gradually poison themselves if the ammonia is not able to dilute itself in a larger ammount of water, as well as be neutralized by cycling your tank. The final point you should consider is this: that goldfish get big...
real big. If they don't have room to grow, they will become stunted...meaning that their organs keep growing but their bodies do not. It is a very sad way for a goldfish to die. The recommended volume of water you should have is for every fish you need 10 gallons. This means you should have your fish in a 40 gallon (or more) tank. If you don't have the room, you should only keep one fish in your 10 gallon tank. Also, it is good to do a 50% water change (including a gravel vacuum) once a week.
Hope this helps!
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