Yes....u can easily reach there by roadway or even by trains
Go for Matheran waterfalls & even you can go for Lonavala or Khandala... they both are neraby
Don't forget to take a ride in Neral-Matheran toy train.
If you enjoy trekking & are nature lover,go for Chanderi caves,Prabalgad Fort..
Or a night stay at Pawana lake
Better go to mahabaleshwar or khandala and lonavala..the ghats are awesome..although rains add beauty to them but they are any ways beautiful..You can get buses,trains,cabs from mumbai to these places
Instead of visiting there u should go to nashik harihar fort... That's the coolest trek and in bucket list of many... So you should check out harihar fort nashik...
You are right, it's a little irrelevant to visit Matheran in this heat and I suggest you give it a shot after it starts raining (if you are still going to be around or in Mumbai)
If you are looking for adventure as well as some leisure time, I have the best option for you..... Check out Bhandardara, dist. Ahmednagar. It's an amazingly beautiful place. It's one of the best place you can visit and chill for 1-2 days. There's mountains all around. Bhandardara is situated in the midst of Sahyadri range. You must visit this place once at least. Check out The Land Of Wanderlust (TLOW) website..... https://thelandofwanderlust.com/