This is a hatmana (insulation) question. I want to know if there is an issue with putting food on the platta on Shabbos day and then putting a thick towel ontop of that food in order for the food to heat up faster and get hotter?
You have three problems here:
- Hatmanah on Shabbat itself
- Mosif hevel -- adding heat
- Hatmanah while it's on the plata (if that's what you're asking about)
All three of those issues make it assur (forbidden). [Shmirat Shabbat C'hilchata 1:65].
However, you can get around problems #1 and #3, as illustrated in the next paragraph.
Hatmanah is only a problem if you cover the entire pot. However, if your cover does not touch the entire thing, it's OK to do even lechatchila (initially) and while it's on the plata. It seems though that you'll have to use something that does not add heat.
Mosif hevel seems to be a problem even when it is fully cooked (see http://vbm-torah.org/archive/cookshabbat/22cookshabbat.htm, quoting Rav Auerbach).
CYLOR before acting on advice given in this answer.