I think it depends upon your definition of mid-term and whether you have a defined use for this money or if it's just a cushion.
I would also have to ask whether you are maxing out your other accounts to get your full benefits.
If you expect to need this money in the next 3 years, then I think you would be wise to put it into a CD ladder / money market fund combination so that you would hopefully at least cover the inflation rate.
This is something that I grappled with quite a bit over the past few years. I'm sure many of us struggle with the loss aversion bias that makes the contemplation of losing money much stronger than the contemplation of gains on that money. Sometimes you just have to grit your teeth and set yourself a minimum safety cushion - whatever it takes to let yourself sleep at night - and make some moves in the mathematically advantageous direction with the rest.
No matter what the math says, you have to work within your own risk tolerance. As you note, you are already doing well to have this conundrum in the first place. Wrestling with where to put all this extra money is a nice problem to have!
Around tax time this year I decided that I had to do something productive with a large cash account balance that I had been carrying for the past few years. I had been maxing out my 401 and Roth accounts, and I had some taxable funds as well, so I was able to rationalize that having a big chunk of cash was the 'prudent' and perhaps even 'strategic' thing to do. After all, the market was at historic highs. The PE10 was getting really up there. A correction or even a bear had to be just around the corner, no doubt waiting for me to put this money into play before pouncing. Isn't it smarter to wait for that correction and then push my chips in at lower valuations?
That little conversation went on in my head for almost 4 years. 4 years of market gains. 4 years of earning .01% return on $100K. Yeah, I hadn't even put it into any CDs because I wanted it to be liquid in case of a big market correction. Even online savings accounts would have been an improvement. But fear makes us stupid.
I finally took some steps this spring. I put a few thousand a month for 3 months into VTSAX and VBTLX funds. This was sort of a dollar-cost-average psychology thing. I moved my sleep-at-night minimum of 20K into a MM fund where I got a $200 bonus (capital One 360 account). This put it on par with a 5 year CD (for this first year, anyway) without locking up those funds. I also put 15K toward my mortgage principal.
I realize that this is probably not the statistically optimal way to distribute that money. But it beats the heck out of leaving it in a savings account.