Edit in JSFiddle

// Global variables. Yeah yeah I know. Just felt like making this one as a procedural program rather than OOP.
var width = 10,
    cells = [],
    cellWidth = 0.01, // 10 centimeters
    cellDepth = 0.01, // 10 millimeter
    cellEdgeArea = cellWidth*cellDepth,
    materialConductivities = {copper: 400, aluminum: 215, brick: 1.3, iron: 80}, // Assume constant. (W / m K)
    materialSpecificHeats = {copper: 390, aluminum: 910, brick: 900, iron: 450}, // Assume constant. (J / kg K)
    materialDensities = {copper: 8940, aluminum: 2712, brick: 2000, iron: 7850}, // Assume constant. (kg / m^3)
    convectionCoefficient = 30, // (W / m^2)
    currentMaterial = 'copper',
    inputHeat = 800, // Watts
    heatAppliedTo = 40, // Cell id#
    initialTemp = 295, // Room temperature. (K) 
    lastTimestamp = null
; 
var createCells = function() {
    var table = $("#plate");
    var index = 0;
    for (var row = 0; row < width; row += 1) {
        var tr = $("<tr>");
        for (var col = 0; col < width; col += 1) {
            var td = $("<td>").attr("id", index);
            tr.append(td);
            cells[index] = initialTemp;
            index++;
        }
        table.append(tr);
    }
};

var keyForNeighbor = function(myKey, whichNeighbor) {
    // whichNeighbor: 0 = north, 1 = east, 2 = south, 3 = west (clockwise)
    if (whichNeighbor === 0 && myKey >= width)
        return myKey - width;
    
    if (whichNeighbor === 1 && ( (myKey + 1) % width !== 0 ) )
        return myKey + 1;
    
    if (whichNeighbor === 2 && myKey < (width*width - width) )
        return myKey + width;
    
    if (whichNeighbor === 3 && myKey % width !== 0)
        return myKey - 1;
    
    return null;
};

var _ = function(id) { 
    return $("#" + id);
};

var cellMass = function() {
    return cellWidth * cellWidth * cellDepth * materialDensities[currentMaterial];
};

var energyTransfer = function(myTemp, yourTemp, dTime) {
    var J = cellWidth * (yourTemp - myTemp) * materialConductivities[currentMaterial] * dTime;
    return J;
    // This is the heat transfer INTO the cell, though general convention is to measure transfer out.
    // Returns the number of Joules transfered into the cell in dTime seconds.
};

var temperatureChange = function(energyIn) {
    var heatCapacity = cellMass() * materialSpecificHeats[currentMaterial];
    return energyIn / heatCapacity;
    // Returns change of temp in K
};

var updateCell = function(id, newTemp) {
    cells[id] = newTemp;
    //_(id).text(Math.round(newTemp));
};

var colorCells = function() {
    for (var i = 0, len = cells.length; i < len; i+=1) {
        var opacity = (cells[i] - initialTemp) / 2000;
        if (opacity > 1) opacity = 1;
        if (opacity < 0) opacity = 0;
        _(i).css("background", "rgba(255,0,0,"+opacity+")");
    };
};

var loop = function() {
    var now = new Date().getTime();
    var dTime = (now - lastTimestamp) / 1000; 
    lastTimestamp = now;
    
    var cellCache = [];
    for (var i = 0, len = cells.length; i < len; i += 1) 
        cellCache[i] = cells[i];
    
    for (var i = 0, len = cells.length; i < len; i += 1) {
        var energyIn = 0;
        var myTemp = cellCache[i];
        for (var n = 0; n < 4; n += 1) {
            var neighborKey = keyForNeighbor(i, n);
            if (neighborKey === null)
                continue;
            var neighborTemp = cellCache[neighborKey];
            energyIn += energyTransfer(myTemp, neighborTemp, dTime);
        };
        
        energyIn -= convectionCoefficient * cellWidth * cellWidth * 2 * (myTemp - initialTemp);
        
        if (i === heatAppliedTo)
            energyIn += inputHeat;

        updateCell(i, myTemp + temperatureChange(energyIn) );
    };
    colorCells();
};
    
$(document).ready(function() {

    lastTimestamp = new Date().getTime();
    createCells();
    $("td").click(function() {
        heatAppliedTo = parseInt($(this).attr("id"));
    });
    setInterval(loop, 20);
    
});

<table id="plate">
</table>

#plate {
    border-collapse:collapse;
    margin:20px auto;
    font-family:"Verdana", "Arial";
    font-size:8px;
    text-align:center;
    color:#CCC;
    border: 1px solid #DDD;
}
    #plate td {
        /*border:1px solid #DDD;*/
        width:20px;
        height:20px;
        overflow:hidden;
    }