I sometimes see in the protocols that perfusion should be conducted with Ice-cold PBS and fixation with Ice cold 4% PFA, in other papers they write that solutions should be in room temperature. Now, which one is better?
The answer depends upon your experimental endpoints. Ice-cold would generally be preferred if phosphorylation measurements will be taken, and is slightly better in terms of preserving nucleotides, but only marginally. It should be noted that some receptors and extracellular proteins are heat-sensitive (e.g. CD62L, IgM) and may be better preserved in membrane with cold PBS.
Room temperature (or 37 degrees) may be preferred in situations requiring rapid ex-vivo tissue transfer. Furthermore, temperature between RT and 37ºC will result in the least response by vasculature in terms of diameter, and may be preferred in situations wherein microvasculature is critical to clear. Think about it: you're changing less, so there will be less response.
This said, ice cold PBS is specified by most labs in most situations, so unless you're seeing suboptimal outcomes directly attributable to temperature, you'd be safe sticking to cold.