Lambda cold start possible solution?

As far as I know this is the only way to keep the function hot right now. It can get pricey only when you have a lot of those functions.

You'd have to calculate yourself how much do you pay for keeping your functions alive considering how many of them do you have, how long does it take to run them each time and how much memory do you need.

But once every 20 minutes is something like 2000 times per month so if you use e.g. 128MB and make them finish under 100ms then you could keep quite a lot of such functions alive at 20 minute intervals and still be under the free tier - it would be 20 seconds per month per function. You don't even need to turn it off after you get a bigger load because it will be irrelevant at this point. Besides you can never be sure to get a uniform load all the time so you might keep your heart beating code active even then.

Though my guess is that since it is so cheap to keep a function alive (especially if you have a special argument that makes them return immediately) and that the difference is so great (10 seconds vs. 80 ms) then pretty much everyone will do it - there is pretty much no excuse not to. In that case I expect Amazon to either fight that practice (by making it hard or more expensive than it currently is - which wouldn't be a smart move) or to make it not needed in the future. If the difference between hot and cold start was 100ms then no one would bother. If it is 10 seconds than everyone needs to work around it.

There would always have to be a difference between running a code that was run a second ago and a code that was run a month ago, because having all of them in RAM and ready to go would waste a lot of resources, but I see no reason why that difference couldn't be made less noticeable or even have few more steps instead of just hot and cold start.

You can improve the cold start time by allocating more memory to your Lambda function. With the default 512MB, I am seeing cold start times of 8-10 seconds for functions written in Java. This improves to 2-3 seconds with 1536MB of memory.

Amazon says that it is the CPU allocation that really matters, but there is no way to directly change it. CPU allocation increases proportionately to memory.

And if you want close to zero cold start times, keeping the function warm is the way to go, as described rsp suggested.