A common mis-perception. ;) Not only can the use of bottom heat post-germination cause leggyness but it also retards root development. In fact it can even "cook" (kill) young roots. So you would be sacrificing root development - which is the most important form of growth at this stage - for top growth. With seedlings, slow top growth is what you are after. That's why professional growers in greenhouses work very hard to maintain air temps of 65 degrees max. Dave

Setup a on demand hot water heater (closed loop) and run a piece of piping through the middle of each bed... set a pump to turn on every X mins/hours to heat the water back up. This would be my suggestion, with the addition of a thermostat, and a 25 gallon plastic barrel as an extra heat soak. I have to admit, I'm heating my tiny Harbor Freight greenhouse with a ceramic heater at the moment, but I have the on demand hot water heater, and the radiant exchangers in place. All I have to do now is learn how to wire up the thermostat,the relay, and the pump without electrocuting myself.

One kilogram of water holds 1.16 watt-hours of heat energy per degree difference in Celsius. That tells you nothing about how fast that heat will be released though, just how much heat energy the water can store when it's at its warmest point. So for example, if the daytime and nighttime temperatures are 30 and 10 degrees Celsius, 1 kilogram of water should be able to hold 2.32 watt-hours of heat that it can release later. That assumes that the water is actually able to heat up to 30 degrees Celsius. If you have a lot of water in there, the temperature of the water may never be able to rise to the ambient temperature inside the greenhouse. The other issue is that as the inside of the greenhouse begins to cool, the water is already going to be releasing energy even when you don't need it. Suppose the temperature inside the greenhouse reaches 32 C and then is wanting to cool down to 25 C. The water is already going to be releasing heat during that time to prevent the inside of the greenhouse from going down to 26. Now suppose the temperature of the water has reached 25 and the temperature inside the greenhouse is reaching towards 17.5 C. The water is still going to be trying to keep the temperature inside the greenhouse from going down to 17.5. That is heat energy that's not going to be there much later in the night when it could be going down to 2 degrees. Depending on the rate of heat transfer, it might not flatten out daytime-nighttime temperatures as much as delay the temperature drop by two or three hours. That might mean if it has dropped down to 3 degrees C by 11pm, the warmest the water is going to be able to keep the greenhouse by 2am (the coldest part of the night) is 3 degrees.

This time of year-almost February- you shouldnt have any frost problems. What might help is to cover around the base of the tree with black plastic or heavy roofing paper. Mangos hate cold wet soil...once summer heats up-remove.