Hot! But you are from Brazil, so you may survive the heat (if you were from Norway, the heat might kill you instantly...)
In and around Moab, it will be very hot, but you should be able to find some crags that are climbable. Basically, be extremely careful to avoid the sun. Climbing in direct sun is absolutely a non-option. Climbing is the shade should be doable; the dry air makes it such that the shade can be pretty comfortable, even when the ambient temperature is way hot.
For cragging near Moab, your best option is Mill Creek. It is in the La Sals, pretty high up, and will be cooler in temperature. Shade can be found. Technical, bolted face climbing (crimps might feel pretty bad in the heat...). The climbing is really good, but it is not your classic desert crack climbing.
If you want more of a desert-splitter experience, there are various crags at Indian Creek that get deep shade and should be climbable. Reservoir Wall is the classic shady crag, but that may still be closed. Other good options exist; others will know better than I. Get an early start so that you don't bake on the hike up.
North faces of towers may be climbable; just make sure that it is actually a north face,i.e. that it isn't a NE face that will get sun int he afternoon Routes on the north side of Castleton (North Face, North Chimney) come to mind. Get a very early start (maybe pre-dawn?) so that you don't die of heat on that talus cone hike up, and take lots of water.
Don't bother going to Wall Street/Potash Road. If you have traveled all the way from Brazil, don't waste your time visiting a mediocre roadside crag next to town; make the extra effort to go the the good stuff.
If it were me, though, I might go somewhere else for at least part of the time. There are dozens of amazing areas in the western US that are in prime season in June- with great climbing and great conditions. Maple Canyon, Rifle, Tensleep, and Wild Iris are some of the classic summer sport areas in that part of the US; you could have a great time at any one of them. Many great trad areas also exist--too many to name, really.
With 20 days, you could definitely spend time in the desert and at one of the cooler (temperature) crags. I might recommend that you start by going to the desert first (it will only get hotter as June progresses), and spend a week chasing the shade and climbing splitters. Maybe start with some time in the Creek getting warmed up, and then go to Castleton. Then, once you get tired of the dry hea, head up to Maple Canyon for some cobbley sport climbing.