Ouch… First mistake! 
Nobody needs 0,0625 degree increments on their temperature readings! The Temperature Conversion Time (the time it takes to get a reading) when using 12 bit resolution is 750 ms per sensor. During this period everything else in your program is pretty much halted (including network). With some creative coding you could circumvent most of the delays, check the code from my “433” project:
https://community.blynk.cc/t/cheap-est-rf-433-mhz-bridge-for-home-automation-with-both-tx-and-rx/
enc28j60 Ethernet module
I would suggest a different Ethernet shield. ENC28J60 is basically crap! 
Some links: