We have two potential convective outbreaks in our near future; the first chance comes tomorrow (Monday) afternoon and evening, in association with a surface cold front. The second opportunity, which has much lower predictability than the first, may arrive Tuesday evening or overnight. Let's begin with tomorrow's threat.
1. High heat and humidity will continue to advect northeastward over the next 24 hours, in advance of a "cool front". Dew points will generally hover in the upper 60s-low 70s with ambient air temperatures in the low to mid 90s. This uncomfortable combination will create an unstable environment, with fairly conducive thermodynamic parameters. MUCAPE values should range from 1000-1500 J/KG, in conjunction with lifted indices of at least -6. In addition, unidirectional shear of 35-40 kts (westerly flow) will aid in convective initiation by the afternoon hours. Low-mid level lapse rates (temp fall with height) are marginal. Surface instability is our biggest component for tomorrow, so any cloud debris could possibly dampen the severe risk. As per usual here in the Northeast, the more sun we can get, the better the chance for more widespread convection. As it is, the primary threat will be strong, damaging winds, via the WLY flow in the mid levels. SPC has a slight risk of severe weather for the Northeast; I believe this is reasonable for tomorrow's threat. Most of us should see T-storms; severe reports will be scattered.
Here's a look at the mesoscale model, NMM, 3-hour precipitation output valid 00z tomorrow (early evening). Notice the T-storms being depicted in eastern PA, which are forecast to move through the tri-state area.

Simulated radar on the NMM for that same time:

2. Tuesday evening/overnight threat: as I noted above, this convection potential has mucher lower predictability, mainly due to the uncertainty in the propagation of mesoscale convective systems (MCSs) more than 12 hours in advance. These T-storm complexes tend to ride along the nrothern periphery of heat ridges, moving eastward and then eastsoutheast with time. The upcoming MCS should develop in advance of a push of a +20c 850mb airmass, which will likely reach the area later in the week in the form of big heat (what's new). The movement and track of this/these MCS events are highly uncertain until they develop, but what I can tell you is that the potential for one to occur in the NYC area becomes quite high Tuesday night.
Note the 588dm height line essentially running W-E along 40 degrees N latitude. Mid level (500mb) winds are generally 40-50 kts along the northern edge of this huge upper level heat ridge. Here's the 00z NAM valid Tuesday evening.

Expect another surge of 1000-1500 J/KG MUCAPE values and higher lifted indices ahead of this MCS. Dew points will remain very sticky, around 70, in conjunction with surface air temperatures near 90F. Conducive thermodynamics in addition to strong westerly, unidirectional winds in the mid/upper levels will yield one or more T-storm complexes which will propagate from the Mid-west into the Northeast over the next several days. Modelling seems to be keying in on the Tuesday overnight time frame as the best potential for the NYC area to see an MCS.
Here's the GFS depiction valid 06z, overnight, Tuesday. Note the precip maximum detected over PA/NJ indicative of MCS potential.

So, in summary:
1. First potential T-storm threat tomorrow afternoon, with the primary threat wind damage (along with locally heavy rain). Confidence on this outbreak higher than the second.
2. Second potential Tuesday evening/overnight in the form of a highly unpredictable MCS, the exact path of which will be uncertain until that time frame (Tuesday afternoon probably). But monitor the situation closely, as probabilities are high for a T-storm complex Tuesday night.
3. All the while, summery weather will continue, with temperatures in the lower to mid 90s and uncomfortable humidity levels.
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