delaro :
If you don't have Thermal paste go find some Zinc Oxide Ointment from a Pharmacy, it will last you about a month and work about the same as cheap thermal paste. A month is about all you will expect out of it though as it will dry out and become ineffective. The base is petroleum jelly which doesn't handle heat for that long.
Another solution is Anti Seize "white zinc oxide stuff" which you can find at any hardware and automotive store it will last a little longer and give you the same results.
You may also be able to find cheap thermal paste at hardware stores or anyplace that deals with residential electronics like Lowes and Menards. You need it on Transformers and other parts in Furnaces.
Yes I have used it in a pinch and it works as a temp solution.
the OP stated they are getting the thermal paste in a few days, not a month.
while this is an option you would still have to clean off this ointment on the CPU and the cooler before you can apply the thermal paste when it arrives.
so again, why risk of braking or making more work for yourself when as you said you will get it soon?