In general, I agree with Naser’s suggestion with some additional considerations. I assume that the cells will be growing and actively proliferating in culture prior to the shift to ambient temp. If you simply feed with fresh media and move such cultures to RT for several days, some cell types will do fine but others will slowly or rapidly lose viability. If your cells are susceptible to viability loss, then it’s best to slow down growth during the RT storage. The simplest way to do this is to do a media change into complete medium with low serum (2%) right before shifting to RT. The cultures should be in flasks, not petri plates or multiwell plates, and should be gassed with 5% CO2 or equilibrated in a CO2 incubator just prior to removing them so that media pH is controlled. Then seal the caps tightly (no filter vent caps), and place flasks somewhere In the dark for RT storage. Prolonged light exposure will damage your cultures, so put them in a box or wrap the flasks in foil.
Some adherent cell types will survive RT storage better if they are first brought just to confluence so that their growth will be contact inhibited. At this point, shift the culture media to low serum (2%), equilibrate CO2, seal flasks and shift to RT. Suspension cultures like HL60 or others cannot be contact inhibited, so just dilute them as for a routine transfer but make the final cell density about twice as high as usual.
If you intend to ship the cells elsewhere, do the above steps and then fill the flasks completely with medium so that shear forces from the air-liquid interface will be minimized during shaking that will occur during shipment.
Many cell culture types can be held at RT safely for up to 2 weeks if you follow these procedures. Note that there will be increasing viability loss over time and that recovery after storage will require 3-7 days until normal growth is resumed.