The following is under the supposition that you are referring to degrees Celsius and the above should be read as +20 °C vs. +4 °C
As chemical processes greatly depend on the temperature your samples will rapidly degrade when being kept at 20 °C. Anyway this temperature may be appropriate if short-term storage is intended and you are interested in features that depend on the temperature.
If you are interested in long(er)-term storage, wanting to keep the samples as unaltered as possible, lower is better. Store the samples at the lowest temperature reliably being above freezing (which would alter the samples significantly). 4 °C seems to be an adequate choice.
please tell us your purpose and we will be able to give you a more precise reply. Are you interested to preserve blood cells (polymorphonuclear? limphocytes? monocytes?) platelets? serum? plasma? whole blood....?
For normal full blood count it can be kept at 4 degrees for a short time. For long time storage and for more investigations it should be divided into different components and can be stored up to -24 degrees.
after collection of blood samples, they should be refrigerated to 4 degree centigrade immediately, in this temperature they are stable for 7 days only. if analysis can't occur within one week then samples should be frozen immediately at -70 degree centigrade.
Never freeze blood tubes if you want to extract gDNA from it... Always extract the maximum amount of gDNA from your samples then you may store it at -70C. But keep in mind freezing of EDTA blood tubes reduces the gDNA extraction quality and quantity.. gDNA extraction from fresh blood is always the best.