The schematic diagram can’t be simpler:

• connect TX of the GY-MCU90640 to RX of the ESP8266;
• connect RX of the GY-MCU90640 to TX of the ESP8266;
• supply the power for both modules (note, that GY-MCU90640 accepts any voltage between 3V and 5V, while ESP module usually requires 3.3V).
  If you use a simpler ESP module (like ESP-01), rather than ESP Dev Board (NodeMCU module), you may have to wire more ESP pins (usually CH_PD and RST must be connected to +3.3v).

Here is a prototype I used for debugging:

Setup (on github):

1. Flash the ESP8266 module with the NodeMCU firmware. If you use older ESP module with small onboard flash (512Kb), you have to configure the NodeMCU firmware to be less than 400Kb. That is required to leave enough space (about 70Kb) on flash file system for Thermal Streamer project files. The easiest way to build smaller firmware is to use NodeMCU custom builds service. When building the firmware, select 1.5.4.1-final (frozen, for 512KB flash) branch and the following modules: CJSON, encoder, file, net, node, timer, UART, WiFi. When the service finish building the firware, it will email you with the two links to download your custom firmware (one for integer version, another for float version). Just download the integer version of custom firmware, check its size (395300 bytes in my case) and flash the ESP module (I used esptool for it).
2. Upload Thermal Streamer project files to ESP flash file system (SPIFFS) using your favorite tool. For example, I used esp-nodemcu-lua-uploader that allows to load all the files in batch mode.
3. Restart the ESP8266 module (turn it off and turn back on). After restarting you will see a new Wi-Fi access point with the name: esp-devlab-setup. You will be able to connect to the module with the default password: We1c0me!. The default Wi-Fi AP name and password are specified in file: connect.lua.
4. On successful connection to the esp-devlab-setup Access Point you will be able to reach the Web UI through the browser by typing anything looking like domain name as an URL, e.g.: any.site.my. You can do that because the software starts a DNS liar server (it responds with the ESP8266 IP to any DNS request) in AP mode.
5. The thermal sensor module has to be initialized. For doing that, you have to navigate to Configure tab of Web UI, and press Setup button in Setup the thermal sensor section. After a couple of seconds, on successful initialization, you will see the message: Turn-off and then turn-on the power to complete setup. That means that the thermal module was initialized and setting are stored in CY-MCU90640 EEPROM. After that, turn-off power supply for both modules, and then turn-on for normal use. That procedure shall be done only once, here is short video: Setup the thermal sensor.
6. Web UI shall be quite self-explaining to use. You only have to remember that the best way to brick the software is to use Web IDE without checking twice what you are uploading to the file system. The changes are taken into account immediately. A bricked NodeMCU can be cured only with connecting of ESP module to computer through UART, formatting of NodeMCU file system, and rewriting the Lua software. In some cases you even have to re-flash the NodeMCU (e.g. if you did the mistake and removed the delay in init.lua.