You likely have a cool season grass like Kentucky bluegrass, fescue, or rye (or a mix). Best time to overseed is late August/early September. You do not want to overseed right now because the new grass will not have enough roots to survive the hot summer. Weeds are also actively growing in the summer and will outcompete the grass. There is less weed pressure in the fall. Fescue can be drought resistant once it's several years old and has developed long roots. Kentucky blue grass (KBG) spreads, so it can fill in bare spots, unlike fescue and rye which stay put. Rye is the quickest to germinate. KBG can take weeks to germinate and is somewhat hard to overseed into other grasses because that other grass is growing and will shade out the seed. You do not need to aerate. Start by killing weeds. You can spot spray with glyphosate. It will kill surrounding grass too but if you're overseeding, the seed will replace that grass. You can seed several days after using it (read the directions). If you use a selective weedkiller, follow the instructions. You may have to wait several weeks to seed. Cut the lawn very low, bagging the clippings. The seed needs to be in contact with the soil so if there are mats of weedy vegetation, remove anything that would prevent the seed from reaching the soil. The seed can be on top of the soil. If you cover it, cover it only very lightly. You can rake a little soil over the seed or use a topdesssing. Or leave it uncovered and walk over the seed to press it in. Spread some starter fertilizer (optional but advisable). Start watering to keep the seed moist all through germination. You will be watering a few minutes several times a day (try 5 minutes 4 times a day and see if that keeps the seed damp). If you're not home in the day and don't have an irrigation system, you can set up hoses and sprinklers and use a timer. As the seedlings emerge, decrease the frequency but increase the amount of water.

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So to reiterate the main point of Becky's reply, wait until August or Sept to do the overseed. In the mean time tolerate the lawn and any weeds you may get.

The reason your grass died after a few days of heat was that the roots were not drought tolerant. You can fix that with proper watering.

Watering: Deep and infrequent is the mantra for watering. This is for all turf grass all over the place. Deep means 1 inch all at one time. Put some cat food or tuna cans around the yard, and time how long it takes your sprinkler(s) to fill all the cans. Memorize that time. That will be the time you water from now on. My hose, sprinkler and water pressure takes 8 full hours to fill the cans. Your time will likely be less. I like gentle watering. As for watering frequency, that depends on the daytime air temperature. With temps in the 90s, deep water once per week. With temps in the 80s, deep water once every 2 weeks. With temps in the 70s, deep water once every 3 weeks. With temps below 70, deep water once a month. Note that you have to keep up with quickly changing temps in the spring and fall. This deep and infrequent schedule works in Phoenix and in Vermont, so it should work for you. The reason for deep and infrequent is to grow deeper, more drought resistant roots and to allow the soil to dry completely at the surface for several days before watering again. If it rains, reset your calendar to account for the rainfall.

When you mow, mow at the mower's highest setting. That will help to develop deeper roots, too. Once your lawn is accustomed to deep and infrequent watering, a couple of days or heat should not affect it at all.