There are many non-connected options with built-in temperature sensors, but when it comes to what you describe, there are only few options for DIY and hobbyists that are not exactly consumer-friendly.
One of the things you could do is get a USB/Serial LCD kit, take one of your 5.25" slot covers, cut a hole and glue it all together. Those screens are programmable, so you will also need to write some sort of script to, for example, feed info from GPU-Z logs to virtual serial port in a proper format (or whatever other info you need to display).
Examples:
https://www.adafruit.com/product/784
http://dangerousprototypes.com/docs/USB_&_serial_LCD_backpack
http://www.plinkusa.net/webplcd525.htm
Or, if you can find one, look for Scythe LCD Master (a ghost of the past):
http://www.scythe.co.jp/en/game/lcd.htm
https://www.phoronix.com/scan.php?page=article&item=140&num=1
...or the one from Silverstone :
https://www.silverstonetek.com/legacy.php?area=en&model=mfp51
...or one of those old retractable 5.25" LCDs:
https://www.thermaltake.com/products-model.aspx?id=C_00000664
Basically, all of the above are a prime example of whattafuck PC enthusiasm was all about back in early 2000s (add weird-shaped CPU cooling and some uber-bright PCIe expansion slot fan and you are good to go)


Regarding custom LCDs:
I've only done this once. Used a regular 20x2 LCD with a custom driver board(ATTiny 2313 + i2c GPIO expansion IC) to display server stats at my old workplace, but that was easy (just redirecting some data from sysfs and other places to serial terminal on Linux).
So, if you want an easy-to-use solution, then you should get a regular rheobus w/ sensors or as R-T-B suggested - a small HDMI display just to show HWInfo or whatever window.