Cold wire...

I recently purchased a Mastech Hy30005D power supply for a Hotwire foam cutter. This unit is working well for lighter 27 gauge wire.  However, I need to use heavier 20 gauge wire for detailed shapes, and this unit seems to be under powered for the task. Could you please guide me in a selection?  Funds are by no means unlimited, but a need a reliable unit that can provide ample heat to cut at a good pace.,

Just for reference, I'm sure this is the unit you purchased? Link

This unit has a max output of 5amps, which is going to be the source of your problems. 

Let's quick reference the nichrome data chart found on my website - Link

As you'll note, for 20 gauge NiChrome wire, 5 amps will generate just shy of 600°F. But for 27 gauge wire, 5 amps will generate just shy of 1800°F!

The thing that I've found is wire temperature and cutting speed are related, but often two different things… 

Most styrofoam products will melt at around 400-600°F, so theoretically a 600°F cutting line should suffice for cutting purposes. But remember, heat has to LEAVE your wire, and enter the sytrofoam to melt and cut the substrate. So your wire has to heat BACK UP in order to cut the next section of foam. Often what people will notice is when the wire FIRST touches the styrofoam it will cut REALLY well, then it will slow down as you get more into the cut.  This is because the heat has left your wire, and the wire is having a hard time heating back up to match your cutting speed. 

The fix is that you need to send more current through your wire. You need to have a hotter over-all wire, to increase your cutting speed. The heating-cooling-heating process will find a happy medium, you just have to find out what that is…

For 20 gauge nichrome, 5 amps will work.. albeit a little slow. For some people, considering the cost, a little slower cut might be acceptable if you have a working product as a trade off.  

From a power supply, I think you would want to have the ability to increase your amperage to 7-8 amps, just so you can play around with your final cutting speed. Here are a few options

30v10a - Link - $94

30v10a - Link - $170

18v10a - Link - $140

Another option would be to select a variac, which is an AC transformer… higher voltage, so be cautious during use

130v20a - Link - $109

130v30a - Link - $134

For the money, I'd select the $94 unit from circuit specialists. It has both a higher voltage (good for small wire) and a higher amperage (good for large wire).