Feasibility of well plate shaker + heater

For my master’s thesis I need to create a well plate shaker with an integrated heater and I am really new to Arduinos.
I found this video with a guide how to create a shaker, but without the heating element. (Here is a demo video: Demo and here ist the full guide at thingiverse: Shaker Guide)
This is the heating element I want to use: Heater Specs, so my questions are:

  • Can the Arduino Micro Pro listed in the components list control the shaker, as well as the heater, a display
    and buttons for the temperature control or do I need another kind of Arduino?

  • What do I need to connect the heater to the Arduino?

Thanks in advance.

Shaker: run a motor with unbalanced load on the shaft.
Heater: how much heat?

Any Arduino can switch a simple relay module ON/OFF. A cheap relay module will conduct 10A of mains AC. With 120VAC you can safely run a 500W motor or heater (maybe need a heat sink/fan) wired for AC. The code would not have to run anything, just switch relays ON/OFF.

Why a heater in a well? Does it freeze down there?

That pdf won't open; it's corrupted it seems. No idea on the heater specs, so can't comment on that.

The video is a small shaker; get an appropriately rated DC motor and use a MOSFET with PWM control. No problem there.

Display and buttons: depends on the display and the number of buttons, but the latter is not likely to be a problem. Consider using an encoder or pot for speed control. Easier to program, easier to handle.