Mimosa Pudica from seed in February.....

Hello-
Hello! I am new here - I don't have a green thumb but I would like to plant some things from seed. I would like to create a greenhouse to grow Mimosa Pudica using the front window shelves in my kitchen. I have attached an image of the space that shows the shelves I would like to use and the amount of light that comes in from both the front and above.
Mimosa Pudica is a tropical plant and needs a warm temperature of 21-24 C. I have purchased a thermometer and the current temp does not go above 19 during the day and of course it drops at night.
What I intend to do is to attached a plastic sheet to the shelves that would be parallel with the wall and create a 'greenhouse'.

Here are my questions for which I hope that you could offer some advice.
Will the window space heat up enough once I place the plastic over the shelves and the plants and soil are inside?
If not will I need a small heater? And if I need a small heater do you have any suggestions?

Thank you in advance for any of your help.

hi Yorkie
Thanks so much for your thoughtful reply!

I don't think that the window is double glazed - either way I think it's just too cold right now - this morning the temp read 17 degrees and the highest it has been is 20.

Thank you for the suggestion of a heated propagator - I have been searching on ebay and will put some bids in today. You are right! They do grow to be quite big. I guess I was thinking that I would start the seeds and see how quickly the plants grow. If they get too big I can put them in larger pots by the window - it should warm up here soon - by the end of March I hope. But that is a very good point that I will keep in mind!

I will let you know how things turn out over the next few weeks. Fingers crossed that this works

I grew sensitive plants from seed very siccessfully a few (OK, lots of) years ago.  They tend to grow straight up, and not bush, so planting a few together might make for a better display.  Although I never transplanted into anything bigger than a 3in put, they grew to a height of about 2' and then flowered quite prolifically.

Now for me to grow them from seed, they must have been very easily germinated, and difficult to kill off, as I would have started them in my bedroom at the time.

I know I ended up giving wuite a lot away as I had so many of them in the end.